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Place Values After the Decimal Point
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Introduction

In this lesson, you will learn about place values after the decimal point. Just as each whole number has a place name, the digits behind the decimal point also have names. The names of the places behind the decimal go in the same order (in the opposite direction) of the whole number place value names. The decimal almost acts like a mirror, reflecting the names back with a slight distortion (for example, tenths place versus tens place).


This video illustrates the lesson material below. Watching the video is optional.


What is a Decimal Point?

A decimal point is the small point that comes after the whole number. Any number to the right of the decimal point shows a portion of a whole number.

The image shows different place values. Before the decimal point, in order from left to right, are the following values: billions, hundred millions, ten millions, millions, hundred thousands, ten thousands, thousands, hundreds, tens, ones. The place values after the decimal, in order from left to right, are: tenths, hundredths, thousandths, ten thousandths, hundred thousandths, millionths, and so on.

Figure 1

In this image you can see that there are many different place values. Before the decimal, in order from left to right (starting with billions), there are the following place values: billions, hundred millions, ten millions, millions, hundred thousands, ten thousands, thousands, hundreds, tens, ones. The decimal falls to the right of the ones place. The place values after the decimal, in order from left to right, are: tenths, hundredths, thousandths, ten thousandths, hundred thousandths, millionths, and so on.

It is important to learn the place value names, both before and after the decimal point. Knowing them will help you know where to round to when someone asks you to round to a certain place value. These names will also help you understand fractions.

Additional Information

In some places around the world, a comma (,) is used to show the decimal point in a number. In other places, a period (.) is used for the decimal point. In this course, a period will be used to mark all decimal points, and sometimes commas will be used to group the numbers to the left of the decimal point for easier reading. If you are used to a comma as your decimal point, be sure to pay close attention to this detail.


Things to Remember


  • Each digit behind the decimal point has a name.
  • The word “and” is used to replace the decimal point when saying the value of the number.

Practice Problems

  1. Consider the number 0.261354. For each of the following digits, give its place value: (
    Video Solution
    x
    Solution:
    a. 1 = thousandths
    b. 2 = tenths
    c. 3 = ten thousandths
    d. 4 = millionths
    e. 5 = hundred thousandths

    Details:

    (Place Value After the Decimal Point #1 (02:50 mins) | Transcript)
    | Transcript)
    1. 1
    2. 2
    3. 3
    4. 4
    5. 5
  2. Consider the number 95.487016. For each of the following digits, give its place value: (
    Video Solution
    x
    Solution:
    a. 6 = millionths
    b. 7 = thousandths
    c. 8 = hundredths
    d. 9 = tens
    e. 0 = ten thousandths

    Details:

    (Place Value After the Decimal Point #2 (02:58 mins) | Transcript)
    | Transcript)
    1. 6
    2. 7
    3. 8
    4. 9
    5. 0

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