## Understand Decimals

The fact that our decimal notation for whole numbers can be extended to represent rational numbers has many important consequences. Key to such an extension is the use of a decimal point to the right of the digit in the ones place. The place-value rule that each digit has a place value equal to 10 times that of the digit to its right can be extended to digits to the right of the decimal point with the following statement. Each digit has a place value equal to one-tenth that of the digit to its left.

This can be represented in the following place-value chart on which the decimal 365.42 appears.

Thousands Hundreds Tens Ones . Tenths Hundredths
10 × 100
or
1,000
10 × 10
or
100
10 × 1
or
10
1

1
× 1
or
or 0.1
×
or
or 0.01
3 6 5 . 4 2

In expanded form, the decimal 365.42 is written

300 + 60 + 5 + + or 300 + 60 + 5 + 0.4 + 0.02
because + = + =

The decimal 365.42 is read three hundred sixty-five and forty-two hundredths. Notice that the decimal point is read as and.

For decimals less than 1, a zero is usually placed to the left of the decimal point, such as in 0.72. However, the zero is not read, so 0.72 is read as seventy-two hundredths. Every decimal can be written as a fraction. For example, 3.75 = 3.

Teaching Model 21.4: Fractions and Decimal Equivalents