What is Point-Slope Form in Math?

What is Point-Slope Form?

Arranging equations in a particular format gives us insight into specific features of an equation. The point-slope form is one such form used with linear equations and is useful when building an equation of a given straight line.

Let’s walk through what the point-slope form is, and learn its use cases with examples.

By the end of this lesson guide, you will be able to construct linear equations in the point-slope form and interpret features like slope, y-intercepts, and x-intercepts.

What are the different forms of linear equations?

A linear equation or an equation of a straight line can be represented in three main forms. These forms are namely:

• Standard form

• Slope-intercept form

• Point-slope form

The major differences between these forms are the way that the properties of a linear equation are presented within the equation. The key properties that are involved in a straight line are the slope and its intercepts (y-intercept and/or x-intercept).

 The standard form, also known as the general form of linear equations, is Ax + By = C, where A, B, and C are constants. Using the standard form to represent a straight line makes it easier to obtain the y and x-intercepts using substitution.

The slope-intercept form is the most commonly used form and is of the form y = mx + b, where m and b are constants. The benefit of using the slope-intercept is that the slope and y-intercept of the straight line can be obtained directly by observing the equation, as m is the slope, and b is the y-intercept.

What is Point-Slope Form?

The point-slope form is another form in which a linear equation with two variables can be represented. As the name suggests, to construct an equation in the point-slope form we require a point on the straight line and its slope.

Definition: The point-slope form of a line is expressed using the slope of the line and point that the line passes through.

Formula: y-y1 = m(x - x1) where m equals the slope of the line and x1 and y1 equal the corresponding x- and y-coordinates of a given point the line passes through.

The general structure of an equation in the point-slope form is: y - y1 = m*(x - x1)

Here (x1,y1) is any arbitrary point on the straight line, and m is the slope/gradient of the straight line. Following is a table that shows a side-by-side comparison of the same straight line represented in the three forms mentioned above.

Again, notice each equation is a different way of expressing the same linear function, namely one with a slope of 2/3 and a y-intercept of 5.

One of the unique properties of the point-slope form compared to the other forms is the flexibility in its structure. This flexibility comes from the fact that you can use any point on a particular straight line to build the point-slope form equation.

In fact, below are some out of infinitely many other valid point-form equations of the straight line above.

• y - 9 = ⅔*(x-6)

• y - 3 = ⅔*(x+3)

• y +1 = ⅔*(x+9)

 Next, let’s find out more about the fundamentals behind the point-slope form.

Fundamentals of the point-slope form

The main concept behind the point-slope form is the formula for determining the slope of a straight line. The formula that is used to calculate the slope of a straight line is :

m = (y2 - y1)/(x2 - x1)

Here, m is the slope of the straight line, while (x1,y1) and (x2, y2) are the coordinates of any two points on the given straight line.

Let’s apply the slope formula to find the slope of the line given in the graph below:

(y - y1)/ (x - x1) = m

Multiply both sides by x - x1, and we get

y - y1 = m * (x-x1), which is the general structure of the point-slope form.

As mentioned before, we can replace (x1,y1) with the coordinates of any point that lies on the given straight line. Note that if you select the y-intercept (b,0), then you will end up with the slope-intercept form of the equation.

y - b = m*(x-0)

y - b = mx

y = mx + b → the slope-intercept form

Therefore, the slope intercept can be considered a special case of the point-slope form.

Now with this fundamental understanding let’s see how we can construct the equation of a straight line in point-slope form using a variety of examples.

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Point-Slope Form Examples

The information provided in a scenario can be different, but the goal is to determine the slope and the coordinates of a point that lies on a straight line.

Example #1 Finding the point-slope equation from slope and a point

Problem: Consider a straight line that has a slope of -7 and passes through the point (5, -3)

We can directly substitute the given data into the point-slope general equation below:

y-y1 = m*(x-x1)

Here m is the slope, hence it is -7 in this example. The point (5,3) is the arbitrary point (x1,y1). By substituting the terms we get:

y - - 3 = -7*(x - 5)

Hence,

y + 3 = -7*(x - 5) is the point-form equation of the straight line.

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Example #2 Finding point-slope equation from two points

Problem: Consider a straight line on which the points (-2,1) and (1,10) lie. Determine the equation of the line in point-slope form.

First, we can use the slope formula to determine m (slope) of the line.

m = (y2- y1)/(x2-x1)

Substituting (-2,1) and (1,10) we get:

m = (10-1)/(1- - 2)

m = 9/3

m = 3

Now that we have determined the slope of the line to be 3, we can build the point-slope equation.

y-y1 = m*(x-x1)

We can pick any point on the line for (x1,y1). Here let’s use (-2,1).

y - 1 =3*(x- -2)

Hence,

y - 1 = 3*(x+2) is the point-form equation of the straight line.

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Example #3 Determining features from the point-slope equation

Problem: Which of the following graphs represents the straight line of equation y - 4 = -2(x + 3)

The equation provided is in the point-slope form. By comparing y - 4 = -2(x+3) and y - y1 = m*(x-x1), we can work out that:

m = -2, and (x1,y1) is (4,-3)

So we must look for a graph that has a slope of -2 and passes through (4,-3). Since only black, red, and blue lines clearly pass through (4,-3), we can eliminate the rest.

Amongst the three, only the black has a negative slope. Hence the line that represents the point-slope equation of y - 4 = -2(x+3) is the black graph.

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Looking for more point-slope form example problems?

Are you ready to extend your thinking and work through 5 more point-slope form practice problems with step-by-step explanations and answers included? Click the link below to access our free guide for students:

⇥ 5 Point-Slope Form Example Problems for Students

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Conclusion: Point-Slope Form

Amongst the three main forms of representing linear equations, the point-slope form can be considered the most versatile. By identifying the slope and a single point that lies on a straight line you can determine the point-slope of an equation. The type of information you get about a straight line may change, hence you should utilize the necessary formulas and/or visual interpretations of graphs to extract what you need.

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5 Point-Slope Form Examples with Simple Explanations

5 Point-Slope Form Examples for Students

When it comes to graphing lines on the coordinate plane, there are several different ways to express a linear equation and figure out how to determine a given line’s slope, y-intercept, points it passes through, and what its graph looks like. Being able to understand and solve problems involving linear equations in various forms, including point-slope form, is an immensely useful and important algebra skills that will help you to solve math problems involving linear equations.

The following lesson will take you step-by-step through solving 5 point-slope formula examples (sample problems) that we will solve and find the final correct answer together. By working through these 5 examples, you will gain a much better understanding of point-slope formula, what it means, and how to use it to solve problems on future homework assignments, quizzes, tests, and exams.

But, before we start working on the point-slope form examples, we will quickly review some very important vocabulary terms and review some key information regarding lines, equations, slopes, and y-intercepts. It is helpful to review this information, even if you are already familiar with it, as you will be building upon it as this lesson progresses and having a strong foundation makes a world of difference.

What is Point-Slope Form?

In math, there are more than one way to express the equation of a line (also referred to as a linear equation).

Most algebra students first learn about slope-intercept form: y=mx+b, where m equals the slope of the line and b equals the y-intercept.

With slope-intercept form, as long as you know the slope and y-intercept of the line, you can determine its equation, graph the line on the coordinate plane, and figure out what points the line passes through.

What is point-slope form?

Definition: The point-slope form of a line is expressed using the slope of the line and point that the line passes through.

Formula: y-y1 = m(x - x1) where m equals the slope of the line and x1 and y1 equal the corresponding x- and y-coordinates of a given point the line passes through.

Unlike slope-intercept form, point-slope form does not require you to know the function’s y-intercept. Instead, you are only concerned with the slope and the coordinates of one point that the line passes through.

If you find this definition confusing, take a look at the graphic below that compares slope-intercept form and point-slope form and further analyze the key similarities and differences between the two forms.

In terms of similarities, both slope-intercept and point-slope form require you to know the slope of the line.

(Looking to learn how to find the slope of a line? click here to access our free guide )

However, the key difference is that slope-intercept form requires you to know the y-intercept of the graph, while point-slope form requires you only to know the coordinates of one point that the graph passes through (this point can be anywhere on the line).

Now that you are familiar with the point-slope form formula, you are almost ready to work through some point-slope form examples. But, before we explore point-slope form further, let’s take a quick look two simple situations involving graphing linear functions using given information.

▶ Situation A: Graph the Linear Function

Problem: Graph a line with a slope of 3 and a y-intercept at 6 and write its equation in y= form.
Notice that Situation A gives us enough information right from the start to write the equation in y=mx+b form since we already know the slope, m, and y-intercept b.

• m=3 and b=6

 We can write the equation as follows:

•  y=3x+6

 This line has a slope of 3 (or 3/1) and a y-intercept at positive 6. We can now graph this line as follows:

Situation B▶: Graph the Linear Function

 Problem: Graph a line with a slope of 3 that passes through the point (2,12) and write its equation in y= form

Notice that situation B does not give us enough information to write the equation of the line in y= form since we only know the slope and not the y-intercept.

 This is where point-slope form comes into play!

In cases like this, m represents the slope, which is 3 and x1 and y1 are the corresponding x- and y-coordinates of whatever given point the line passes through.

Since we already know that the line passes through the point (2,12), we know that x1=2 and y1=12 

We can substitute these values into the point slope formula as follows

 After substituting m=3, x1=2, and y1=12, you end up with the following equation in point-slope form:

• y-12 = 3(x-2) 

If we want to graph the line on the coordinate plane, it may be easier to rearrange this formula into y=mx+b form as follows:

To convert from point-slope form to slope-intercept form:

• y-12=3(x-2) ➞ y-12=3x-6 ➞ y=3x+6

Now that we have converted the equation into y=mx+b form, we can go ahead and graph this line since we know that the slope is 3 and the y-intercept is positive 6.

Notice that the line does pass through the point (2,12).

What else do you notice about this graph? It turns out that situation A and situation B both represent the same linear equation, just in different forms.

• Situation A: slope-intercept form

• Situation B: point-slope form

If you are comfortable with solving problems involving equations in y=mx+b form (slope-intercept form), then you can surely be successful at solving problems involving point-slope form (y-y1=m(x-x1).

To take this next step, practice is key! So, now let’s look at 5 examples of solving algebra problems involving point-slope form to give you some more experience.

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Point-Slope Form Example #1

Problem: Determine the point-slope form of a line that has a slope of 1/2 and passes through the point (8,2).

To determine the equation of this line in point-slope form, you have to know the following pieces of information:

• the slope of the line, m

• the coordinates of a point that the line passes through, (x1, y1)

In this first example, both of these pieces of information are given to you, so you are ready to write the equation of the line in point-slope form by substituting m=1/2, x1=8, and y1=2 as follows:

Answer: The equation of the line in point-slope form is: y-2=1/2x(x-8)

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Point-Slope Form Example #2

Problem: Determine the point-slope form of a line that has a slope of 3/4 and passes through the point (4,-6).

Again, to determine the equation of this line in point-slope form, you have to know the following pieces of information:

• the slope of the line, m

• the coordinates of a point that the line passes through, (x1, y1)

Just like example #1, both of these pieces of information are given to you, so you are ready to write the equation of the line in point-slope form by substituting m=3/4, x1=4, and y1=-6 as follows:

In this example, the value of y1 is a negative number (-6). When you substitute this value into the point-slope formula, on the left-side of the equation, you end up with: y - - 6

You can simplify this double-negative by rewriting it as a positive: y- -6 ➞ y + 6

Answer: The equation of the line in point-slope form is: y+6=3/4x(x-4)

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Point-Slope Form Example #3

Problem: Determine the point-slope form of a line that passes through the points (1,10) and (3,16)

Just like the previous two examples, to determine the equation of this line in point-slope form, you have to know the following pieces of information:

• the slope of the line, m

• the coordinates of a point that the line passes through, (x1, y1)

Unlike the first two examples, in this case you are not given all of the required information upfront. While you know that coordinates of a point that the line passes through (you actually know two of them), you do not know the slope of the line.

Luckily, you can use the slope formula to find the slope of a line that passes through two given points.

The slope formula is equal to change in y over change in x.

To correctly use the slope formula, you have to correctly label and identify the (x1, y1) and (x2, y2) values so you can substitute them into the formula. The first point that you use will have the 1’s and the second point that you identify will have the 2’s.

• (1) First Point: (x1,y1) ➞ (1,10) where x1=1 and y1=10

• (2) Second Point: (x2,y2)➞ (3,16) where x2=3 and y2=16

You are now ready to calculate the slope as follows:

By substituting the values of (x1,y1) and (x2,y2) into the slope formula, you end up with :

• m = (16-10)/(3-1) = 6/2 = 3

After simplifying 6/2 to 3, you can conclude that the slope of the line, m, equals 3

Now that you know the slope of the line and the coordinates of a point that the line passes through, you can write the equation of the line in point-slope form. Note that you can choose either given point that the line passes through (1,10) or (3,16). Below, we will use the first given point (1,10):

Answer: The equation of the line in point-slope form is: y-10=3(x-1)

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Point-Slope Form Example #4

Problem: Determine the point-slope form of a line that passes through the points (-5,15) and (-10,18)

Again, in order to determine the equation of this line in point-slope form, you have to know the following pieces of information:

• the slope of the line, m

• the coordinates of a point that the line passes through, (x1, y1)

Just like in example #3, you are not given all of the required information upfront. While you know that coordinates of a point that the line passes through, you do not know the slope of the line.

Following the same process as example #3, you can use the slope formula to determine the value of m as follows:

By substituting the values of (x1,y1) and (x2,y2) into the slope formula, you end up with :

• m = (18-15)/(-10- -5)

Notice that the double negative in the denominator can be rewritten as: (-10- -5) ➞ (-10 + 5)

• m = (18-15)/(-10 + 5) = 3/-5

You can express these results as -3/5, so you can conclude that the slope of the line, m, equals -3/5

Now that you know the slope of the line and the coordinates of a point that the line passes through, you can write the equation of the line in point-slope form. Just like the last example, you can choose either given point that the line passes through (-5,15) or (-10,18). Below, we will use the first given point (-5,15):

Answer: The equation of the line in point-slope form is: y-15=-3/5(x+1)

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Point-Slope Form Example #5

Problem: Graph the line with the following point-slope form equation: y-4=2(x+6)

In this final example, you will have to graph a line and all that you are given is a linear equation in point-slope form.

All that you need to graph a line is the slope of the line and a point that the passes through—which is exactly what you can find when you look at the equation in point slope form.

Remember that point slope form is as follows: y-y1 = m(x = x1) where m equals the slope of the line and (x1,y1) are the corresponding x- and y-coordinates of the point the line passes through.

So, in this example, we can see that the slope of the line m=2 (or 2/1)

Furthermore, we can see that the y1=4, but what about x1?

Since we see that ‘+’ sign on the right-side of the equation (x+6), we know that a double-negative must have occurred, so the x1 value is equal to -6 (not positive 6).

Now we have all of the information that we need:

• Slope: m=4

• Point: (x1,y1) = (-6,4)

All that we have to do now is graph the line. Start by plotting the (x1,y1) point, which is (-6,4) in this example as follows:

Next, use the slope m=2/1 to “build” more points by using the rise over run method (rise two units, and run two units to the right) as follows:

Finally, draw the line that intersects the points that you plotted to complete your graph:

Answer:

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Calculating Percent Decrease in 3 Easy Steps

Calculating Percent Decrease in 3 Easy Steps

Being able to calculate percent decrease is an extremely useful and important numerical skill that can has implications far beyond the math classroom. An ability to calculate, understand, and analyze percents will not only help to excel on quizzes, tests, and examples, but in real world situations as well. While students often believe that calculating percent decrease to be challenging task, the process to getting correct answers is actually very easy and straightforward.

(Looking for a Percent Decrease Calculator to make a super-fast calculation: Click here to access our free Percent Decrease Calculator)

The following free Calculating Percent Decrease step-by-step lesson guide will walk you through calculating percent decrease using an easy and simple three-step method. By learning to follow these three steps, you will be able to quickly and accurately solve problems in math involving percent decrease.

Before we start learning about calculating percent decrease and the three-step method, lets perform a fast review of a few important math vocabulary terms and concepts related to this topic.

Looking to learn how to calculate percent increase or percent change? Use the links below to download our free step-by-step guides:

• How to calculate the percent increase between two numbers

• How to calculate the percent change between two numbers

Percent Definition

In mathematics, the term percent refers to parts per one hundred and the mathematical symbol for percent is %.

For example, the value 40% is defined as 40 per 100. If you observe the below diagram, you will see that the blue shaded region makes up 40% of the entire grid.

We can also say that percent represents a ratio of a value out of one hundred.

Another example would be 20% meaning 20 out of every 100. Looking at percent as a ratio, when can say that if 20% of 300 students have an exam on Monday, then 60 total students have an exam on Monday (20 out of every hundred means three 20’s out of 300 total students).

Percent Decrease Definition

The next question we have to ask is what is the meaning of percent decrease?

In mathematics, the percent decrease between two values is the difference between the final number and the initial number (which we will refer to as the starting number in this guide). Percent decrease is always expressed as a percentage of the starting number.

Note that percent decrease is a value that will be expressed as a percentage and will include the % symbol.

For example, if you had $80 dollars in savings at the start of the month and $60 in savings by the end of the month and you needed to calculate the percent decrease, the final number would be 60 and the starting number would be 80.

Being able to correctly identify the starting number and the final number is extremely important when it comes to correctly solving percent decrease problems.

Calculating Percent Decrease

Now it’s time for you to learn how to calculate percent decrease using our simple three-step method.

Let’s revisit the previous scenario involving money in your savings account decreasing between the start of the month and the end of the month:

Calculating Percent Decrease Example #1

For the first example, let’s find the percent decrease for the following scenario:

If a total amount in your savings account of $80 at the start of the month had decreased down to $60 by the end of the month, what is the percent decrease?

Here is how you can apply our three-step method:

Step 1: Find the difference of the values by subtracting the final value from the starting value.

In this example, the difference of starting value and the final value can be calculated as follows:

80 – 60 = 20

In this case, the difference of the two values would be 20. Note that, when calculating percent decrease, you will always be subtracting the smaller value from the larger value.

Step 2: Divide the difference by the starting number.

The next step is to take the difference (20 in this example) and divide it by the starting number (80 in this example) as follows:

20/80 = 0.25

Always express your answer as a decimal (this is crucial for performing your final calculation in Step 3).

Step 3: Multiply by 100

The third and final step is to multiply the decimal result from Step 2 by 100 and then express that result as a percent using the % symbol.

0.25 x 100 = 25

Final Answer: 25% Decrease

You’re done! By using the three-step method, you can conclude that there was a 25% decrease in how much money you had in savings from the start of the month to the end of the month.

Need more help? No worries. Let’s move onto another example where we will calculate percent decrease using the same three-step method.

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Looking for a free Percent Decrease Calculator?

If you need a faster way to calculate the percent decrease between two numbers, check out our free Percent Decrease Calculator tool, which lets you input the starting and final values to get an instant answer!

▶ Click here to access our free Percent Decrease Calculator for students

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Calculating Percent Increase Example #2

Last week, Zoe sold a total of 51 chocolate cupcakes at her bakery. This week, she sold a total of 34 chocolate cupcakes at her bakery. What was the percent decrease in the total amount of chocolate cupcakes sold between last week and this week?

To solve this problem, note that the starting value is 51 and the final value is 34.

Step 1: Find the difference of the values by subtracting the final value from the starting value.

In this example, the final value minus the starting value can be calculated as follows:

51– 34 = 17

Step 2: Divide the difference by the starting number.

For step two, take the difference (17 in this example) and divide it by the starting number (51 in this example) as follows:

17/51 = 0.3333333…

Notice that the result is a repeating/non-terminating decimal. You can round this result to the nearest hundredths decimal place to make things easier. In this case, you can round the result to 0.33

Step 3: Multiply by 100

The last step is to multiply the decimal result from step two by one hundred and express the final result as a percent. So…

0.33 x 100 = 33

 Final Answer: 33% Decrease

We’re all finished! We have concluded that there was a 33% decrease in the total amount of chocolate cupcakes sold at Zoe’s Bakery between last week and this week.

After this first example, you should be feeling more confident about your ability to correctly calculate percent decrease e using the three-step method. Let’s gain some more experience by looking at another example.

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Calculating Percent Decrease Example #3

Last school year, 414 students attended the Delta High School Winter Ball This year, only 112 students attended the Delta High School Winter Ball. What was the percent decrease in students who attended the Winter Ball between last year and this year?

 Just like the last two examples, you can solve this problem by following the three-step process:

Step 1: Find the difference of the values by subtracting the starting value from the final value.

 In this example, the starting value minus the final value can be calculated as follows:

414– 112 = 302

Step 2: Divide the difference by the starting number.

Let’s continue with step two as follows:

Find the difference (190 in this example) and divide it by the starting number (414 in this example) as follows:

302/414 = 0.7294685…

Just like in example 2, you can round the result to the nearest hundredths decimal place to make things easier. In this case, you can round the result to 0.73

Step 3: Multiply by 100

The last step is to multiply the decimal result from step two by 100 and express the final result as a percent. So…

0.73  x 100 = 73

Final Answer: 73% Decrease

At this point, you should feel much better about your ability to calculate percent decrease and solve any math problems involving percent decrease our three-step method. But, if you feel like you need more practice, it is highly recommended that you work through examples one through again on your—be sure to do the problems by hand and take notes as you go along!

Conclusion: Calculating Percent Decrease

You can calculate percent decrease given any two values by using the following 3-step method:

Step 1: Find the difference of the values by subtracting the final value from the starting value.

Step 2: Divide the difference by the starting number. Express result as a decimal.

Step 3: Step 3: Multiply by 100. Express result as a %.

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What about Calculating Percent Increase and Percent Change?

Learn how to calculate a percent increase or a percent change between two numbers using our free step-by-step guides. Click the links below to get started.

⇥ Calculating Percent Increase in 3 Easy Steps

⇥ Calculating Percent Change in 3 Easy Steps

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Don’t forget about our Free Percent Decrease Calculator

Click here to get started using our free Percent Decrease Calculator

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Are You Using This Genius Strategy for Math Writing?

Image Source: Mashup Math MJ

Writing about math helps kids to organize their thinking, use key vocabulary, and communicate mathematically—which leads to deep and meaningful understanding.

Over the past few years, math teachers are incorporating more writing activities into their lesson plans—a trend that is being driven by the use of highly engaging think-notice-wonder writing prompts that spark deep mathematical discussion and are highly effective as warm-up or cool-down activities. 

This strategy has recently been endorsed by the National Council of Teachers of Mathematics:

By asking What do you notice? What do you wonder? we give students opportunities to see problems in big-picture ways, and discover multiple strategies for tackling a problem. Self-confidence, reflective skills, and engagement soar, and students discover that the goal is not to be "over and done," but to realize the many different ways to approach problems.

How does it work?

Math teachers often struggle to find topics for their kids to write about. Sometimes the best way to encourage creativity and exploration is simply posting an image and asking students to describe what they think, notice, and wonder about what they are seeing.

The best way to use think-notice-wonder activities is to choose an image every day and project it as large as you can at the front of your classroom.

Then, have students write 3 sentences about the image starting with:

      •     I think…

      •     I notice…

      •     I wonder…

✔  You may want to have students share their entries in a daily math journal. This practice will get them used to writing about mathematics regularly.

✔  Try not to give too many prompts. You’ll be surprised by how creative and detailed student responses will become over time!

✔  Try to choose images that work with the day’s topic/theme

What would think-notice-wonder look like in YOUR classroom?

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Image: Mashup Math MJ

Imagine an unusual day where your kids enter class expecting a normal warm-up practice problem but are caught by surprise.

They see the above image of a drone delivering a package displayed on the board along with a writing prompt that calls for them to complete the statements I think..., I notice..., and I wonder...

What kind of creative thoughts and ideas would they have?

How much weight can the drone carry? How many packages can it hold at once?

How would thinking about this image activate their prior knowledge and spark their curiosity?

What are the dimensions of the largest and smallest box it can hold? Does it have to be square?

What kind of anticipation would it build for an upcoming lesson or activity?

Does the drone use GPS coordinates to get from point to point?

Why Think-Notice-Wonder?

Engaging in think-notice-wonder writing activities at the start of a math class is a great way to ignite student thinking, spark creativity, and build anticipation.

Even if students are not directly engaged in mathematical problem-solving, their curiosity and interest will carry on throughout the day’s lesson.

Be mindful that your kids will need some time to get used to these kinds of activities, but after a week or so, you’ll be pleasantly surprised by the spike in engagement, boost in student enthusiasm and high quality of responses!

Are you ready to try it with your kids?

Here are a few more sample graphics for you to try in your classroom:

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Want more? Download 101 Daily Think-Notice-Wonder Writing Prompts for Engaging Your Kids

You can now share 101 Daily Think-Notice-Wonder Writing Prompts with your kids with our PDF workbook!

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Do you have experience using think-notice-wonder activities with your math students? Share your thoughts and suggestions in the comments section below!

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By Anthony Persico

Anthony is the content crafter and head educator for YouTube's MashUp Math and an advisor to Amazon Education's 'With Math I Can' Campaign. You can often find me happily developing animated math lessons to share on my YouTube channel . Or spending way too much time at the gym or playing on my phone.

Where is the hundredths place value in math?

Where is the hundredths decimal place in math?

In math, when we look at numbers, we can assign something called place value to each digit based on the position of each number.

When learning about and analyzing numbers—ranging from simple single-digit numbers all the way up to extremely large numbers that can have ten digits or more or—it is important that you understand the meaning of the significance of each digit’s place value, especially when decimals are involved.

When you first start learning about place value, determining each digit’s place value can be simple, especially when you are dealing with integers and decimals are not involved. However, once decimals are in play, identifying place value can get a bit trickier.

This free and simple guide for students will focus on the hundredths place and can be used as a quick review to help you along your place value journey when you start working with numbers involving decimals.

Once you understand place value, you will gain a deeper understanding of numbers—large and small—and your mental math and operational skills (performing addition, subtraction, multiplication, division, and more) will surely improve.

Are you ready to get started?

What is place value?

Before we learn about the hundredths place and what it means in terms of place value, let’s do a super quick review of some key vocabulary terms and some things that you may already know.

Definition: In math, place value refers to the numerical value that a digit has by virtue of its position in the number.

For example, consider the number 2.5.

We can think of the number 2.5 as the sum of 2 ones and 5 tenths.

So, in terms of place value, we can say that for the number 2.5:

•  2 is in the ones place

• 5 is in the tenths place

Pretty simple, right? Now, let’s extend this understanding of place value to the hundredths place.

 What is the hundredths place?

In our last example, we looked at 2.5, which is a relatively simple decimal. As numbers grow larger, you will have to identify larger types of place values.

For example, consider the number 2.54.

We can express the number 2.54 as the sum of 2 ones, 5 tenths, and 4 hundredths.

So, in terms of place value, we can say that for the number 2.54:

•  2 is in the ones place

• 5 is in the tenths place

• 4 is in the hundredths place

In these previous examples, we are essentially deconstructing each number to identify the place value of each digit.

Note that the tenths place is different than the tens place and the hundredths place is different than the hundreds place.

 The chart below shows you each place value position relative to a decimal point.

For example, consider the number 539.25

We can insert this value into the chart as follows:

Using the chart, we can clearly see that

• 5 is in the hundreds place

• 3 is in the tens place

• 9 is in the ones place

• 2 is in the tenths place

• 5 is in the hundredths place

 Be sure not to confuse the hundreds place with the hundredths place!

Hundredths Decimal Place Examples

Now let’s go ahead and look at some more examples of determining which number is in the hundredths decimal place of a given number.

Example #1: Which digit is in the hundredths decimal place?

216.325

 We can input this value into our chart as follows.

Using the chart, it is easy to see that the value in the hundredths place is 2.

 216.325

 Answer: 2

Example #2: Which digit is in the hundredths decimal place?

0.791

We can input this value into our chart as follows.

Using the chart, it is easy to see that the value in the hundredths place is 9.

0.791

Answer: 9

Example #3: Which digit is in the hundredths decimal place?

2,056.178

We can input this value into our chart as follows:

Using the chart, it is easy to see that the value in the hundredths place is 7.

2,056.178

Answer: 7

Example #4: Which digit is in the hundredths decimal place? 67.33333…

We can input this value into our chart as follows.

Using the chart, you can see that the hundredths place is 3.

Answer: 3

Example #5: Which digit is in the hundredths decimal place?

515.2

Notice that, at first glance, there is no value in the hundredths place.

However, 515.2 can also be expressed as 515.20

We can input this value into our chart as follows.

Using the chart, you can see that the hundredths place is 0.

Answer: 0

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Extra Practice Problems

Which value is in the Hundredths Decimal Place?

By now, you should be more comfortable with identifying numbers occupying the hundredths decimal place.

Below, you will find 10 practice problems that will give you an opportunity to test your understanding of the hundredths place.

If you would like to use a chart to help you, click the link below to download a free blank place value chart!

▶ FREE DOWNLOAD: Decimal Place Value Chart (PDF File)

Practice Problems: Determine which number is in the hundredth place for each of the following:

 (Answer key to follow!)

1)   2.75

2)   56.333

3)   8.18

4)   403.212

5)   5,009.15

6)   0.04

7)   0.0004

8)   76.5333

9)   565.404

10)  10,214.133

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Finished? Don’t scroll further until you are ready to see the answer key.

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Answer Key

1)     2.75

2)     56.333

3)     8.18

4)     403.212

5)     5,009.15

6)     0.04

7)     0.0004

8)     76.5333

9)     565.404

10)10,214.133

Conclusion: Hundredths Decimal Place

In math, each digit position in any given number has its own unique place value “slot.” These positions or “slots” are referred to as place value.

While determining place value positions for integers can be relatively simple, the identification process becomes trickier when decimals values become involved.

Using a chart can be a helpful tool to help you to correctly identify place value for numbers that one, two, three, or more digits after a decimal point.

Namely, the hundredths decimal place refers to the second digit to the right of the decimal point.

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Keep Learning: Free Math Guides