## Divide Decimals

Division of Decimals
The division algorithm for dividing a decimal by a whole number is similar to the division algorithm for whole numbers. An example of dividing money can be used to illustrate this.

Divide \$56.34 equally among 6 individuals. How much does each person receive? Think of the \$56.34 as five \$10 bills, six \$1 bills, three dimes, and four pennies.

If the divisor and dividend are multiplied by the same number, the quotient remains the same. If you are dividing apples equally among a group of children and triple both the number of apples and the number of children, then the number of apples per child stays the same. This is the principle used when dividing by a decimal. Use multiples of 10 to convert the division by a decimal into a problem of dividing by a whole number.

23 ÷ 3.2 = 230 ÷ 32
452.893 ÷ 0.23 = 45,289.3 ÷ 23
Multiply by 10.
Multiply by 100.

Such conversions are usually shown as

The quotient of two decimals can always be written as a quotient of whole numbers. For example, the quotient 452.893 ÷ 0.23 = 452,893 ÷ 230 (multiply both the dividend and the divisor by 1,000).

Repeating and Terminating Decimals
All fractions represent division and thus can be written as decimals. However, not all division ends, or terminates. A terminating decimal occurs when the division has a remainder of 0. An example is 1 ÷ 2 = 0.5. Fractions like cannot be represented by a terminating decimal. The decimal equivalent for is 0.333…. This means the threes continue on and on indefinitely since there is always a remainder of 1. A complete explanation of why = 0.333… requires an understanding of infinite sums and is beyond most students in elementary school. However, students do understand patterns and can see the patterns that occur in repeating decimals. A repeating decimal occurs when a pattern of numbers repeats indefinitely after the decimal point and the numbers are not all zeros. In writing repeating decimals, a bar is placed over the pattern of numbers that repeats. Thus,

Teaching Model 14.7: Divide a Decimal by a Decimal