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Introduction to Place Values
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Introduction

In this lesson, you will learn about place values for whole numbers and how to say large numbers in English.


These videos illustrate the lesson material below. Watching the videos is optional.


Place Values

Place value is the value a digit has due to its location within a number. Without place value, you may think that $1 is worth the same amount of money as $100, because they both have a one in them.

Place value is important when doing arithmetic. Understanding place value allows you to regroup numbers when you subtract, multiply, or divide, and properly estimate and round numbers.

Here are the names of place values in American English:

A box displaying the number 6,731,239,465. Above each number are the names of each place value. Above the five on the far right is the word “ones.” To the left of it above the six is says, “tens.” To the left of that, above the 4 is says, “Hundreds.” Continuing left above each number is says: Thousands, Ten Thousands, Hundred thousands, Millions, Ten millions, hundred millions, and Billions.

Figure 1

From smallest to largest, these place values include the following:

  • Ones
  • Tens
  • Hundreds
  • Thousands
  • Ten Thousands
  • Hundred Thousands
  • Millions
  • Ten Millions
  • Hundred Millions
  • Billions

The place values continue after billions, but this list is sufficient for the purposes of this lesson.

Each place value represents a group. For example, the tens place value represents the number of groups of ten. In the number 465, there are six groups of 10. Likewise, there are four groups of 100.

Practicing Place Values

Practice identifying the place values of the following numbers.

Example 1
137

The figure shows groups of cubes that makes up a total of 137.

Figure 2

Start with the ones place. In 137, there are seven ones in the ones place. This is represented by seven individual cubes. Next is the tens place. In 137, there are three sets of ten. Because items in the tens place are grouped into sets of ten, the picture above shows three sets of ten cubes. Last is the hundreds place. In 137, there is a one in the hundreds place, which means there is one group of 100.

Notice that 10 groups of 10 cubes make up a group of 100.

Example 2
1483

A group of cubes that makes up a total of 1,483.

Figure 3

Now look at the number 1483, or one thousand four hundred eighty-three.

Start with the ones place. In 1483, there is a three in the ones place, which is represented by the three individual cubes. In the tens place, is an eight, which indicates the number 80 and is represented by eight sets of ten cubes. In the hundreds place there is a four, which represents four groups of 100. If you zoom in on the picture, you can see that there are ten groups of ten cubes, or 100 cubes, in each of the four sets. In the thousands place there is a one. This means there are 1000 cubes in this place. 1000 is made of ten groups of 100 cubes.

How to Say Large Numbers in English

Saying large numbers is easier when you start by saying smaller numbers. For example:

A box displaying the number 6,731,239,465. Above each number are the names of each place value. Above the five on the far right is the word “ones.” To the left of it above the six is says, “tens.” To the left of that, above the 4 is says, “Hundreds.” Continuing left above each number is says: Thousands, Ten Thousands, Hundred thousands, Millions, Ten millions, hundred millions, and Billions.

Figure 4

First look at the three numbers at the very end: 465, which is said, “four hundred sixty-five.” Notice that you say the place value for the hundreds column, but 65 is said on its own. You don’t need to say a tens or ones place value because they are both implied or understood, but you do want to include the group place value name when you say a large number, such as thousands or millions.

Practice saying the number listed in the figure above. When saying large numbers, always start on the left-hand side.

  • In the billions section there are just six billion, because there aren’t any numbers in the ten billions or hundred billions places.
  • In the millions section there are seven hundred thirty-one million.
  • In the thousands section there are two hundred thirty-nine thousand.
  • In the hundreds section there are four hundred sixty-five.

Put all together, you would say this number as “six billion, seven hundred thirty-one million, two hundred thirty-nine thousand, four hundred sixty-five.”


Things to Remember


  • Place value is the value a digit has due to its location within a number.
  • Ten groups of ten make 100, and ten groups of 100 make 1000.
  • When saying large numbers, always begin on the left-hand side.

Practice Problems

  1. Consider the number 7,986,035,214. What is the place value for each number? (
    Solution
    x
    Solution:
    a. 1 tens
    b. 2 hundreds
    c. 3 ten thousands
    d. 4 ones
    e. 5 thousands

    Details:
    A box displaying the number 7,986,035,214 and above each number stating the name of each place value

    a. The number 1 is in the tens place. Located between 2-hundreds and 4-ones.
    7,986,035,214

    b. The number 2 is in the hundreds place. Located between 5-thousands and 1-ten.
    7,986,035,214

    c. The number 3 is in the ten thousands place. Located between 0-hundred thousands and 5-thousands.
    7,986,035,214

    d. The number 4 is in the ones place. The last number on the right, next to 1-ten.
    7,986,035,214

    e. The number 5 is in the thousands. Located between 3-ten thousands and 2-hundreds.
    7,986,035,214
    )
    1. 1
    2. 2
    3. 3
    4. 4
    5. 5
  2. Consider the number 7,986,035,214. What is the place value for each number? (
    Video Solution
    x
    Solution:
    a. 6 millions
    b. 7 billions
    c. 8 ten millions
    d. 9 hundred millions
    e. 0 hundred thousands

    Details:

    (Introduction to Place Values #2 (02:00 mins) | Transcript)
    )
    1. 6
    2. 7
    3. 8
    4. 9
    5. 0
  3. Consider the number 3,562,907,148. What is the place value for each number? (
    Solution
    x
    Solution:
    a. 3 billions
    b. 2 millions
    c. 0 ten thousands
    d. 1 hundreds
    e. 5 hundred millions

    Details:
    a. 3 is in the billions. You can also say you have three 1,000,000,000s.
    Notice there are nine numbers after the 3.
    3,562,907,148

    b. 2 is in the millions place. You have two 1,000,000s.
    Notice there are six numbers after the 2.
    3,562,907,148

    c. 0 is in the ten thousands. You can say you have zero 10,000s.
    Notice there are four numbers after the 0.
    3,562,907,148

    d. 1 is in the hundreds, so you have one 100.
    Notice there are two numbers after the 1.
    3,562,907,148

    e. 5 is in the hundred millions. You have five 100,000,000s.
    Notice there are eight numbers after the 5.
    3,562,907,148
    )
    1. 3
    2. 2
    3. 0
    4. 1
    5. 5
  4. Consider the number 3,562,907,148. What is the place value for each number? (
    Video Solution
    x
    Solution:
    a. 6 ten millions
    b. 9 hundred thousands
    c. 7 thousands
    d. 4 tens
    e. 8 ones

      Details:

      (Introduction to Place Values #4 (01:52 mins) | Transcript)
      )
      1. 6
      2. 9
      3. 7
      4. 4
      5. 8

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