Question

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}

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asked 2020-11-09
Which of the following fractions are repeating decimals and which are terminating? How made decisions? \(a) \frac{2}{15}\)
\(b)\frac{11}{20}\)
\(c)\frac{17}{40}\)
\(d)\frac{1}{12}\)

Answers (1)

2020-11-10

Given: The following fractions: \(a) \frac{2}{15}\)
\(b)\frac{11}{20}\)
\(c)\frac{17}{40}\)
\(d)\frac{1}{12}\) 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, \(0.1 \overline{3}\)
\({,15 } 20\)
\(-15\)
\(\_\)
\(050\)
\(-45\)
\(\_\)
\(05\) 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. \(b) \frac{11}{20}\) Using long division method, \(\_ \_ \_() \underline{0}.55\)
\(20 ) 110\)
\(-100\)
\(\_\)
\(0100\)
\(-100\)
\(\_\)
\(000\)
\(\_\) 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. \(c) \frac{17}{40}\) Using long division method, \(\_\_\_()\underline{0.}425\)
\(40 ) 170\)
\(-160\)
\(\_\)
\(0100\)
\(-80\)
\(\_\)
\(200\)
\(-200\)
\(\_\)
\(000\)
\(\_\) 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. \(d) \frac{1}{12}\) Using long division method, \(\_ \_ \_() \underline{0}.08\overline{3}\)
\(12 )100\)
\(- 96\)
\(\_\)
\(40\)
\(- 36\)
\(\_\)
\(04\)
\(\_\) 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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