Which of the following fractions are repeating decimals and which are terminating? How made decisions? a) frac{2}{15} b)frac{11}{20} c)frac{17}{40} d)frac{1}{12}

Braxton Pugh 2020-11-09 Answered
Which of the following fractions are repeating decimals and which are terminating? How made decisions? a)215
b)1120
c)1740
d)112
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Expert Answer

Gennenzip
Answered 2020-11-10 Author has 96 answers

Given: The following fractions: a)215
b)1120
c)1740
d)112 To find which of the following fractions are repeating decimals and which are terminating. The non-terminating decimals(repeating decimals): The non-terminating decimals are those which keep on continuing after decimal point. The terminating decimals: The terminating decimals are those which come to an end after few repetitions after decimal point. a) 215 Using long division method, 0.13
,1520
15
_
050
45
_
05 A number 3 after the decimal point is repeating since the remainder 05 is there at the end of the long division. Therefore, the fraction has the repeating decimals. b)1120 Using long division method, ___()0.55
20)110
100
_
0100
100
_
000
_ There is an end after few repetitions after decimal point since the remainder is zero at the end of the long division. Therefore, the fraction has the terminating decimals. c)1740 Using long division method, ___()0.425
40)170
160
_
0100
80
_
200
200
_
000
_ There is an end after few repetitions after decimal point since the remainder is zero at the end of the long division. Therefore, the fraction has the terminating decimals. d)112 Using long division method, ___()0.083
12)100
96
_
40
36
_
04
_ A number 3 after the decimal point is repeating since the remainder 04 is there at the end of the long division. Therefore, the fraction has the repeating decimals.

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