Write as a decimal. 1 2 1. (answer: 0.5) 7 5 2. (answer: 1.4) 9 4 3. Pre - Algebra Bench Mark 7 Know Rational Numbers Are Either Terminating Or Repeating Decimals Warm Up Write as a decimal. 1 2 1. (answer: 0.5) 7 5 2. (answer: 1.4) 9 4 3. (answer: 2.25) 3 8 4. (answer: 0.375)

Know Rational Numbers Are Either Terminating Or Repeating Decimals Pre - Algebra Bench Mark 7 Know Rational Numbers Are Either Terminating Or Repeating Decimals Vocabulary: rational number number that can be expressed as a ratio of two integers terminating decimal number when expressed as a decimal has a finite decimal expansion; also called a regular number repeating decimal number when expressed as a decimal has a ‘final’ set of digits which repeat an infinite number of times; also called a recurring decimal period the number of recurring digits in a repeating decimal; also called the repetend vinculum a horizontal line placed over the recurring digits in a repeating decimal

Know Rational Numbers Are Either Terminating Or Repeating Decimals Pre - Algebra Bench Mark 7 Know Rational Numbers Are Either Terminating Or Repeating Decimals It is obvious that terminating decimals are rational numbers. For example, 0.75 = = 75 100 3 4 0.625 = = 625 1000 5 8 and 0.6 = = 6 10 3 5 It is much less evident that repeating decimals are also rational numbers. For example, 1 9 = 0.1111, 1 6 = 0.1666 and = 0.363636 4 11 So we can see that repeating decimals are also rational numbers.

Know Rational Numbers Are Either Terminating Or Repeating Decimals Pre - Algebra Bench Mark 7 Know Rational Numbers Are Either Terminating Or Repeating Decimals The real challenge will be to write a fraction in simplest form given a repeating decimal. To illustrate, lets make up a repeating decimal such as 0.606060. We will name our number a = 0.606060 and multiply it by a power of 10, then subtract the original a and the new number so that the repeating decimal parts cancel each other in the subtraction. a = .606060 and multiply it by a power of 10, 10a = 6.06060 The decimals do not line up so try multiplying by 100. 100a = 60.6060 The decimals line up and the repeating parts will cancel. 100a = 60.606060 a = 60 99 20 33 = - a = 0.606060 20 33 So, 0.606060 = 99a = 60 Solve for a and reduce.

Find the period of the repeating part of . . 9 9 9 Divide. 11 1.0 - 99 Pre - Algebra Bench Mark 7 Know Rational Numbers Are Either Terminating Or Repeating Decimals Example 1 11 Find the period of the repeating part of . . 9 9 9 Divide. 11 1.0 - 99 1 - 99 1 - 99 1 We can see that 2 digits (0 and 9) are repeating so the period is 2.

Classify the decimal as repeating or terminating. Pre - Algebra Bench Mark 7 Know Rational Numbers Are Either Terminating Or Repeating Decimals Practice 4 9 a. Convert 0.4444 to a fraction in simplest form. (answer: ) b. Find the period of the repeating part of . (answer: 2 ) 32 33 13 11 c. Write as a decimal. (answer: 1.1818; repeating) Classify the decimal as repeating or terminating. 19 18 d. Convert 1.0555 to a fraction in simplest form. (answer: )

(answer: 0.875; terminating) Pre - Algebra Bench Mark 7 Know Rational Numbers Are Either Terminating Or Repeating Decimals Quiz 7 8 1. Write as a decimal. (answer: 0.875; terminating) Classify the decimal as repeating or terminating. 14 9 2. Convert 1.5555 to a fraction in simplest form. (answer: ) 3. Find the period of the repeating part of . (answer: 1) 2 3 99 101 4. Convert 0.98019801 to a fraction in simplest form. (answer: ) 5. Find the period of the repeating part of . (answer: 4) 85 101