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Evaluating Algebraic Expressions 2-1Rational Numbers California Standards NS1.5 Know that every rational number is either a terminating or a repeating decimal and be able to convert terminating decimals into reduced fractions. NS1.3 Convert fractions to decimals and percents and use representations in estimations, computations, and applications.

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Evaluating Algebraic Expressions 2-1Rational Numbers rational number terminating decimal repeating decimal Vocabulary

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Evaluating Algebraic Expressions 2-1Rational Numbers A rational number is any number that can be written as a fraction, where n and d are integers and d 0. n d Any fraction can be written as a decimal by dividing the numerator by the denominator. If the division ends or terminates, because the remainder is zero, then the decimal is a terminating decimal.

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Evaluating Algebraic Expressions 2-1Rational Numbers If the division leads to a repeating block of one or more digits (where all digits are not zeros) after the decimal point, then the decimal is a repeating decimal. A repeating decimal can be written with a bar over the digits that repeat. So 0.13333… = 0.13.

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Evaluating Algebraic Expressions 2-1Rational Numbers 9 11 The pattern repeats. 1 –9.2 2 0.0 2 11 9 –1 8 Additional Example 1A: Writing Fractions as Decimals Write the fraction as a decimal. The fraction is equivalent to the decimal 1.2. 11 9

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Evaluating Algebraic Expressions 2-1Rational Numbers This is a terminating decimal. 20 7.3 05 The remainder is 0. 7 20 –0 7 1 0 0 0 0.0 0 –6 0 –1 0 0 Additional Example 1B: Writing Fractions as Decimals Write the fraction as a decimal. The fraction is equivalent to the decimal 0.35. 7 20

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Evaluating Algebraic Expressions 2-1Rational Numbers 9 15 The pattern repeats, so draw a bar over the 6 to indicate that this is a repeating decimal. 1 –9.6 6 0.0 6 15 9 –5 4 Write the fraction as a decimal. Check It Out! Example 1A The fraction is equivalent to the decimal 1.6. 15 9

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Evaluating Algebraic Expressions 2-1Rational Numbers 40 9 This is a terminating decimal..2 02 The remainder is 0. 9 40 –0 9 1 0 0 0.0 0 –8 0 – 8 0 2 0 0 0 5 0 – 2 0 0 Write the fraction as a decimal. Check It Out! Example 1B The fraction is equivalent to the decimal 0.225. 9 40

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Evaluating Algebraic Expressions 2-1Rational Numbers To write a terminating decimal as a fraction, identify the place value of the digit farthest to the right. Then write all of the digits after the decimal point as the numerator with the place value as the denominator.

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Evaluating Algebraic Expressions 2-1Rational Numbers 5.37 A. 5.37 7 is in the hundredths place, so write hundredths as the denominator. 37 100 = 5= 5 Additional Example 2: Writing Terminating Decimals as Fractions Write each decimal as a fraction in simplest form. 0.622 B. 0.622 2 is in the thousandths place, so write thousandths as the denominator. 622 1000 = = 311 500 Simplify by dividing by the greatest common divisor.

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Evaluating Algebraic Expressions 2-1Rational Numbers A fraction is in reduced, or simplest, form when the numerator and the denominator have no common divisor other than 1. Remember!

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Evaluating Algebraic Expressions 2-1Rational Numbers 8.75 A. 8.75 5 is in the hundredths place, so write hundredths as the denominator. 75 100 = 8= 8 = 8= 8 3434 Simplify by dividing by the greatest common divisor. Write each decimal as a fraction in simplest form. Check It Out! Example 2 0.2625 B. 0.2625 5 is in the ten-thousandths place. 2625 10,000 = = 21 80 Simplify by dividing by the greatest common divisor.

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Evaluating Algebraic Expressions 2-1Rational Numbers x = 0.44444…Let x represent the number. Additional Example 3: Writing Repeating Decimals as Fractions Write 0.4 as a fraction in simplest form. 10x = 10(0.44444…) Multiply both sides by 10 because 1 digit repeats. Subtract x from both sides to eliminate the repeating part. Since x = 0.44444…, use 0.44444… for x on the right side of the equation. _ 10x = 4.444444… x = 0.44444… 9x = 4 9x = 4 9 9 Since x is multiplied by 9, divide both sides by 9. x = 4949

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Evaluating Algebraic Expressions 2-1Rational Numbers x = 0.363636…Let x represent the number. Check It Out! Example 3 Write 0.36 as a fraction in simplest form. 100x = 100(0.363636…) Multiply both sides by 100 because 2 digits repeat. Subtract x from both sides to eliminate the repeating part. Since x = 0.363636…, use 0.363636… for x on the right side of the equation. __ 100x = 36.363636… x = 0.363636… 99x = 36 99x = 36 99 99 Since x is multiplied by 99, divide both sides by 99. x = = 36 99 4 11 Write in simplest form.

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