Exercise Use long division to find the quotient. 180 ÷ 15

Exercise Use long division to find the quotient. 3 ÷ 5

Exercise Use long division to find the quotient. 3 ÷ 12

Exercise Use long division to find the quotient. 1 ÷ 3

Exercise Use long division to find the quotient. 7 ÷ 11

, ( ) Rational Numbers can be expressed as a ratio: 3 4 2 1 2 , ( ) 3 4 2 1 2 can be expressed as a decimal: 0.75, 2

When a rational number is expressed as a decimal, the digits either terminate or repeat.

1 3 2 5

Example 1 3 4 Convert to a decimal. 4 3.00 0.75 2 8 20 3 4 = 0.75

Example 2 5 12 Convert to a decimal. 5 12 = 0.416666… = 0.416 0.416 5 12 Convert to a decimal. 12 5.000 0.416 4 8 20 12 80 72 8 5 12 = 0.416666… = 0.416

Example 3 2 11 Convert to a decimal. 11 2.00 0.18 1 1 90 88 2 2 11 2 11 Convert to a decimal. 11 2.00 0.18 1 1 90 88 2 2 11 = 0.181818… = 0.18

Example Convert the fraction to a decimal. 7 20 = 0.35

Example Convert the fraction to a decimal. 7 3 = 2.3

Example Convert the fraction to a decimal. 4 33 = 0.12

Example Convert the fraction to a decimal. 11 24 = 0.4583

Example Convert the fraction to a decimal. 5 7 = 0.714285

To convert terminating decimals to fractions: place the digit(s) that follow(s) the decimal point over the place value of the last digit and reduce to lowest terms.

Example 4 Convert 0.175 to its reduced rational form using the GCF. 175 1,000 = 7 x 25 40 x 25 7 40 =

Example Convert 0.12 to a fraction in lowest terms. 12 100 3 25 =

Example Convert 3.25 to a fraction in lowest terms. 325 100 13 4 =

To convert repeating decimals to fractions: Set the decimal equal to x. Multiply the equation by 10n, where n = the number of repeating digits. Subtract 1. from 2. Reduce.

Example 5 0.45

Example 6 0.136

0.3

0.7

0.342

0.571, 0.579, 0.57, 0.6, 0.571, 0.5714, 0.59