Place Value

In this lesson, you will learn

  • What place value means and why each place is worth 10 times the place to its right
  • How to show a number with place value blocks
  • The names of the places up to the hundred-millions place
  • How to find the place and the value of any digit in a number

What Is Place Value?

Definition

The place value tells you the value of each digit in a number.

In our numeration system, the digits that we use are any of the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

Rule

The value of each place is equal to 10 times the value of the place to its right.

Notice that each digit has a place and a value, thus the name place value.

The first place on the right has a value of 1. The second place from the right has a value of 10. The third place from the right has a value of 100, and so forth...

Place value blocks: 1 thousand is a large cube equal to 10 hundreds, 1 hundred is a flat equal to 10 tens, 1 ten is a rod equal to 10 ones, and 1 one is a small cube

The figure above shows only 4 places and these are the ones place, the tens place, the hundreds place, and the thousands place. The number that the figure above represents is 1111.

The number 1111 with arrows from each digit: 1 thousand, 1 hundred, 1 ten and 1 one

How many tens make 1 hundred?

Show answer

10 tens. Each place is worth 10 times the place to its right, so 1 hundred = 10 × 1 ten.

How to Show a Number With Place Value Blocks

How would you write down the number 3248 using the place value blocks?

Place value blocks for 3248: 3 thousand cubes, 2 hundred flats, 4 ten rods and 8 one cubes

3248 is equal to 3 thousands, 2 hundreds, 4 tens, and 8 ones.

  • The number 8 is in the ones place and it has a value of 8.
  • The number 4 is in the tens place and it has a value of 40.
  • The number 2 is in the hundreds place and it has a value of 200.
  • The number 3 is in the thousands place and it has a value of 3000.
Common mistake

Giving the digit instead of its value. In 3248, the digit 4 is in the tens place, so its value is 4 tens = 40, not 4.

What is the value of the 5 in 2,517?

Show answer

500. The 5 is in the hundreds place, so its value is 5 hundreds = 500.

Place Value of Big Numbers

For big numbers such as 250,785,864, we show the place values with the figure below. Study the names of the places for each digit starting with 4.

Place value chart for 250,785,864 that names the place of each digit, from the ones place on the right to the hundred-millions place on the left

Looking at the number, you can see that 7 is in the hundred-thousands place and 2 is in the hundred-millions place.

It also means that the value of 7 is 7 hundred thousand or 700,000 and the value of 2 is 2 hundred million or 200,000,000.

Remember

Count the places from the right: ones, tens, hundreds, thousands, ten-thousands, hundred-thousands, millions, ten-millions, hundred-millions.

In 250,785,864, which digit is in the ten-millions place, and what is its value?

Show answer

5, with a value of 50,000,000. The ten-millions place is the 8th place from the right.

More Examples Showing How to Find the Place Value

Find the name of the place and the value for each underlined digit

579

9 is in the ones place and it has a value of 9.

9877

9 is in the thousands place and it has a value of 9000.

5698746

6 is in the hundred-thousands place and it has a value of 600,000.

67892456

7 is in the millions place and it has a value of 7,000,000.

34521663987

2 is in the ten-millions place and it has a value of 20,000,000.

8962212352

1 is in the ten-thousands place and it has a value of 10,000.

Worked example: Find the place and the value of the 3 in 4,639,105.
  1. Start at the right and name each place: 5 is in the ones place, 0 in the tens place, 1 in the hundreds place.
  2. Keep going to the left: 9 is in the thousands place and 3 is in the ten-thousands place.
  3. The value of the 3 is 3 ten-thousands: 3 × 10,000 = 30,000.

3 is in the ten-thousands place and it has a value of 30,000.

In 81,402, what is the place and the value of the 1?

Show answer

The thousands place, with a value of 1,000. From the right: 2 is in the ones place, 0 in the tens, 4 in the hundreds and 1 in the thousands.

Summary

  • The place value tells you the value of each digit in a number.
  • Each place is worth 10 times the place to its right: ones, tens, hundreds, thousands, and so on.
  • The value of a digit is the digit times the value of its place. In 3248, the 4 has a value of 40.
  • To find the place of a digit, count the places from the right.

Test Yourself: Interactive Place Value Quiz

Click the digit in the place that the question asks for. You have 10 seconds for each number, and a fast answer earns bonus points. The quiz ends when you run out of time 3 times.

High score on this device: 0

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