Place Value: Whole Numbers and Decimals

Contributor: Ashley Nail. Lesson ID: 13103

How big is a number, really? Learn how to identify the place and value of a digit within a number. Then, play a game to showcase your place value skills!

categories

Elementary

subject
Math
learning style
Visual
personality style
Lion, Beaver
Grade Level
Intermediate (3-5)
Lesson Type
Quick Query

Lesson Plan - Get It!

Audio:

3,716.842

That is a big number! That is approximately how many miles you would have to swim if you crossed the Atlantic Ocean! But how do we really understand that 3,716.842 is a big number? On paper, it just seems like a random order of numbers with commas and periods.

But if you were a professional swimmer and wanted to take on the challenge of swimming across the Atlantic Ocean, you would absolutely want to understand the value of that number!

By using our knowledge of place value, we can really wrap our minds around how much swimming we would need to do!

Before we break apart the number 3,716.842, let's back up and find the value of a smaller number.

  • You wouldn't swim across a whole ocean without practicing first, would you?

You swim laps in a pool to practice. Every time you swim a mile, you put a circle in your training notebook.

By the end of the day, you have a lot of circles drawn in your notebook.

number of miles

To find out how many miles you just swam, you count the circles. You count 23 circles, so you swam 23 miles today at practice.

If you look at your notebook again, you notice that there are two groups of 10 circles, which equals 20 altogether.

20 miles

Therefore, when we look at the number 23; we can determine that the 2 is in the tens place and has a value of 20.

20

Look at your notebook one more time. After we make groups of 10, there are still 3 more circles. These represent the ones.

3 miles

When we look back at 23, we know that 3 is in the ones place and has a value of 3 ones, which is just 3.

3

The number 23 was easy because there were no commas or decimals! The same idea applies even when we have bigger numbers. We just need to know the language to find the place value of other numbers.

Look at the place value chart for whole numbers.

place holder chart

You get better at your training, and you swim 1,942 miles. Let's look at the 2 first.

  • We know that the 2 is in the ones place and has a value of 2.

Next, look at the 4.

Now, we'll look at the 9. If we look back at the chart, we know that the hundreds place is next. We also know if we were keeping track of miles in our notebook, like before; once we had enough tens to make a hundred, we would move to circling groups of 100.

  • So, the 9 must be in the hundreds place and have a value of 900!

Now, you try the last number. Look at the 1.

completed place holder chart

Now, let's say you were practicing swimming in a pool. You got tired and didn't swim a whole mile. You only swam part of a mile. The value of that part mile is represented by a fraction. The numbers are placed to the right of the decimal point.

Look at the chart below.

place holder chart

You only swam 0.547 miles.

  • The 5 is in the tenths place and has a value of 5/10 of a mile.
  • When I look at the chart, I can see that the 4 is in the hundredths place and has a value of 4/100.

Your turn. Look at the 7.

completed place holder chart

Now that you can find the place values of numbers with multiple digits and decimals, you can try to really understand the distance across the Atlantic Ocean! Visit the Got It? section to see if you can figure it out!

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