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Chapter 4—Decimals

4-1 Naming Decimals

 When you complete the work for this section, you should be able to: Describe where decimal fractions fall on a number line. Identify the three main parts of a decimal fraction. Identify decimal place values from tenths to millionths.

Decimal numbers, like fractions, allow us to express fractional parts of a number—including places between the integer values on the number line.

In the example shown here, you can see two different points (shown in blue) on a number line that do not fall directly on the integer values. One of the values in this example is between –3 and –2, and the other is somewhere between +2 and +3.

Decimal numbers can be located between the integer values
on a number line.

 Definition There are three parts to a decimal number: An integer A decimal point A decimal fraction A decimal consists of an integer and a decimal fraction, separated by a decimal point.

Example

Here are the three parts of the decimal number, 2.14

Decimal fractions play the same roles in mathematics as the numerator-and-denominator fractions that you have already studied in these lessons. However, you will soon discover that decimal fractions are much more useful and far easier to work with.
 .

This counter runs continuously from decimal value 1.00 to 9.99.

Naming Decimal Place Values

Just as whole numbers and integers have place values, so do decimal numbers.

 Review This figure shows the seven place values for a typical whole-number value. You've seen this before: ones, tens, hundreds, thousands, ten-thousands, and so on. All New A Decimal number has three parts, including a whole-number part. And, just as before, the whole-number part has place values called tens, hundreds, thousands, and so on. But the decimal fraction part is different.

In a decimal number, the decimal point is the starting point for determining place values. Place value on the left side of the decimal point are the whole-number values. Place values on the right side of the decimal point are the decimal-fraction place values.

• Place values for the whole-number part of a decimal number begin with ones and increase in the left-hand direction.
• Place values for the decimal fraction part of a decimal number begin with tenths and increase in the right-hand direction.

You can see that the names for the whole-number and decimal-fraction parts of a decimal number are very similar. Whereas whole-number place values are called tens, hundreds, thousands, and so on, decimal-fraction place values are called tenths, hundredths, thousandths, and so on.

Names for the place values found in decimal fractions.

 Whole-Number Part Decimal-Fraction Part tens tenths hundreds hundredths thousands thousandths ten-thousands ten-thousandths hundred-thousands hundred-thousandths millions millionths ten-millions ten-millionths hundred-millions hundred-millionths

 Note There is no equivalent of a 1's place in the fraction part of a decimal number. There is a 1's place in the whole-number part, but not in the decimal part.

Examples

1. The shaded number in 23.148 is in the hundredths place.
2. The shaded number in 1.596 is in the thousandths place.
3. The shaded number in 159.19003 is in the hundred-thousandth place.

Examples and Exercises

 Names of Decimal Places Use these interactive examples and exercises to strengthen your understanding and build your skills.

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