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English2.8SpanishWriting Fractions as DecimalsHow can you tell from the denominator of aSSTATESTANDARDSfraction if its decimal form is terminating or repeating?MA.6.A.5.11EXAMPLE: Writing a Fraction as a DecimalWrite the fraction as a decimal. Is it terminating or repeating?38a. —3. Place the decimal pointdirectly above the decimalpoint you placed in Step 1.0.3753.0008 )‾1. To divide 3 by 8, placea decimal point after 3. 2460 5640 4002. Place as many zeros asnecessary to complete thedivision.38The division terminates. So, — 0.375 is a terminating decimal.23b. —1. To divide 2 by 3, placea decimal point after 2.3. Place the decimal pointdirectly above the decimalpoint you placed in Step 1.0.6662.0003 )‾ 1820 1820 1822. Place as many zeros asnecessary to see a patternin the remainder.23The division does not end. So, — 0.666. . . is a repeating decimal.Inductive ReasoningWrite the fraction as a decimal. Is it terminating or repeating?3476. —202. —90Chapter 211677. —83. —Multiplying and Dividing Fractions1658. —124. —29219. —405. —

EnglishSpanishUse estimation to match the fraction with its decimal. Then use a calculator tocheck your answer.561310. —A. 0.6255831611. —12. —13. —B. 0.1875C. 0.333 . . .D. 0.83333 . . .1714. In — 0.1428571428571428571 . . . , what are the repeating digits?Can you find another fraction that has at least six digits that repeat?15. a. Describe the denominators of fractions that can be written asterminating decimals.b. Describe the denominators of fractions that can be written asrepeating decimals.16. IN YOUR OWN WORDS How can you tell from the denominator of a fraction if itsdecimal form is terminating or repeating?17.18.The Mayan number system was base 20. In a base 20 system,describe the denominators of fractions that would be representedby terminating decimals and by repeating decimals.012345678910111213141516171819The Babylonian number system was base 60. In a base 60system, describe the denominators of fractions that would be representedby terminating decimals and by repeating 203040505954555657Use what you learned about writing fractions as decimals tocomplete Exercises 11–18 on page 94.Section 2.8Writing Fractions as Decimals91

English2.8SpanishLessonLesson TutorialsWhen writing a fraction as a decimal, your result is a terminating or repeatingdecimal. A repeating decimal repeats a pattern of one or more digits.Key Vocabularyrepeating decimal,p. 9212Terminating decimal: — 0.52—Repeating decimal: — 0.666 . . . 0.63Show that a decimal repeats by using three dotsor placing a bar over the digit that repeats.Method 1: Writing Fractions as DecimalsTo write a fraction as a decimal, divide the numerator by thedenominator.EXAMPLE1Writing Fractions as Decimals1856a. Write — as a decimal.b. Write — as a decimal.Place the decimal point.Place the decimal point.ReadingOne way to say therepeating decimal—0.83 is “zero pointeight three, with thethree repeating.”0.1251.0008 )‾ 820 1640 4000.833)‾6 5.000 4820 1820 182Place zeros to completethe division.Remainder is 0. Thedecimal terminates.18Place zeros tosee a pattern inthe remainder.The remainder 2keeps repeating.56— 1 8 0.125Write the fraction as a decimal. Is it terminating or repeating?352.—9204.—1. —3. —92Chapter 2Multiplying and Dividing Fractions—— 5 6 0.833 . . . or 0.831985

EnglishSpanishMethod 2: Writing Fractions as DecimalsTo write a fraction as a decimal, write an equivalent fraction(if possible) whose denominator is 10, 100, or 1000.EXAMPLE2Writing a Fraction as a Decimal320Write — as a decimal.20 is a factorof 100.EXAMPLE3Because 20 5 100, multiply thenumerator and denominator by 5.3 520 5320— —15100 —Multiply. 0.15— is read as “fifteen hundredths.”15100Real-Life Application2125You run the 40-yard dash in 6 — seconds. Your teammate runs itin the time shown. Who is faster and by how much?2125Write 6 — as a decimal and compare it to 6.9.212521256— 6 —Write the mixed number as a sum.Because 25 4 100, multiply thenumerator and denominator by 4.21 425 4 6 —84100 6 —Multiply. 6 0.84 6.84— is read as “eighty-four hundredths.”841006.84 6.9. The difference is 6.9 6.84 0.06 second.So, you are faster by 0.06 second.Write the fraction as a decimal.Exercises 11– 265.45—11206. —750472507. —8. —379. In Example 3, Pedro runs the 40-yard dash in 6 — seconds.50Is he the fastest? Explain.Section 2.8Writing Fractions as Decimals93

EnglishSpanishExercises2.8Help with Homework1. NUMBER SENSE When using division to write a fraction as a decimal, whendo you stop dividing?2. WHICH ONE DOESN’T BELONG? Which fraction does not belong with the otherthree? Explain your reasoning.1415—16——18—Tell whether the decimal is repeating or terminating.——5. 7.43. 0.6254. 0.136. 0.470Rewrite the repeating decimal using bar notation.7. 0.1111 . . .8. 3.4444 . . .9. 0.5333 . . .10. 0.1666 . . .6) 39 (- 3) 3 (- 9) 4 (- 1)9 (-Write the fraction as a decimal.171012. —15. —171816. —19. —32020. —193024. —2 11. —23. —5613. —315014. —234017. —212518. —71821. —3822. —514025. —1142526. —27. ERROR ANALYSIS Describe and correct the error in8writing — as a decimal.1551628. GOLDFISH The length of a goldfish is — foot. Writethe length of the goldfish as a decimal.29. BASEBALL Your batting average for a baseball season111521511456252215 0.533 . . .8—8.00015 )‾— 0.531575504550455is —. Write your batting average as a decimal.Copy and complete the statement using , , or .7830. —94Chapter 20.8551231. —0.4Multiplying and Dividing Fractions32. 1.953920—

EnglishSpanishWrite the number as a fraction. Then write the fraction as a decimal.33. five-eighths34. eleven-twelfths35. nine-fourteenths36. sixty-three twentieths37. OPEN-ENDED Find a fraction whose decimal value is between 0.5 and 0.65.Write the fraction and its decimal equivalent.38. ENDANGERED SPECIES The table shows shell lengths of four sea turtles thaties list of Florida.are on the endangered speciesSea TurtleShell LengthngthGreen2 — fttHawksbill2 — ftKemp’s Ridley2 — fttLeatherback2 — ftt92019110511a. Convert the shell lengthss to decimalsdecimals. Then order the shell lengthsfrom least to greatest.b. How much longer is the leatherback sea turtle than the green sea turtle?39. PATTERNS Use the following pattern.09— 0.000000 ,19— 0.111111 ,3929— 0.222222 . . .99a. Complete the pattern for — through —.b. Two of the decimals in the pattern have terminating decimal forms.One is 0.000000 . . . , which is simply 0. The other is 0.999999 . . . .What is the terminating form of this decimal? Explain your reasoning.Write the fraction as a decimal.11533340. —11533,30041. —100180001001800,00042. —43. —Use rounding to estimate the sum or difference. SKILLS REVIEW HANDBOOK44. 4.8 6.445. 10.7 3.846. 2.16 7.4447. 16.58 5.2648. MULTIPLE CHOICE Which expression is equivalent to 9(3 x 5)?A x 32 B 9x 32 C 9x 72 Section 2.8SECTION 1.4D 27x 45 Writing Fractions as Decimals95

Section 2.8 Writing Fractions as Decimals 93 Method 2: Writing Fractions as Decimals To write a fraction as a decimal, write an equivalent fraction (if possible) whose denominator is 10, 100, or 1000. Write 3 — 20 as a decimal. 3 — 20 — 3 5 20 5 15 — 100 M