## Add and Subtract Decimals

**Comparing and Rounding Numbers**

To compare decimals, students begin by comparing digits in each place value, starting at the left, until different digits appear. The number with the greater value digit in that place is the greater number. For example, when comparing 0.28 and 0.21, students note that the digits in the tenths place are the same but the digits in the hundredths place are different. The fact that 8 > 1 implies that 0.28 > 0.21. Students should also realize that 8 > 1 can be written as 1 < 8, which implies that 0.21 < 0.28.

Place-value concepts are also applied when rounding decimals. When rounding to a place such as tenths, students look at the digit in the place to the right, the hundredths place. If that digit is 5 or greater, the decimal is rounded to the next tenth, otherwise the digit in the tenths place is not changed. When rounding to a decimal place, all digits to the right of the rounded place are dropped. For example, 6.0835 rounded to the nearest tenth is 6.1, to the nearest hundredth is 6.08, and to the nearest thousandth is 6.084.

**Addition and Subtraction of Decimals**

The algorithms that were used for addition and subtraction of whole numbers can also be used for addition and subtraction of decimals. Digits are aligned according to place value, which means that the decimal points should be aligned. Then computation is completed from right to left.

Add the hundredths. |
Add the tenths. |
Add the ones. |
Add the tens. |

11 hundredths = 1 tenth + 1 hundredth |
16 tenths = 1 one + 6 tenths |
13 ones 1 tens + 3 ones. |

When subtracting, appending one or more zeros after the decimal point may make computation easier. Subtract 17.32 from 31.5.

Append a zero. Regroup. Subtract the hundredths. |
Subtract the tenths. | Regroup. Subtract the ones. |
Subtract the tens. |

**Teaching Model 22.4:** Add and Subtract Decimals