# 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}

Which of the following fractions are repeating decimals and which are terminating? How made decisions? $a\right)\frac{2}{15}$
$b\right)\frac{11}{20}$
$c\right)\frac{17}{40}$
$d\right)\frac{1}{12}$
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Given: The following fractions: $a\right)\frac{2}{15}$
$b\right)\frac{11}{20}$
$c\right)\frac{17}{40}$
$d\right)\frac{1}{12}$ 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, $0.1\stackrel{―}{3}$
$,1520$
$-15$
$\mathrm{_}$
$050$
$-45$
$\mathrm{_}$
$05$ 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. $b\right)\frac{11}{20}$ Using long division method, $\mathrm{_}\mathrm{_}\mathrm{_}\left(\right)\underset{―}{0}.55$
$20\right)110$
$-100$
$\mathrm{_}$
$0100$
$-100$
$\mathrm{_}$
$000$
$\mathrm{_}$ 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. $c\right)\frac{17}{40}$ Using long division method, $\mathrm{_}\mathrm{_}\mathrm{_}\left(\right)\underset{―}{0.}425$
$40\right)170$
$-160$
$\mathrm{_}$
$0100$
$-80$
$\mathrm{_}$
$200$
$-200$
$\mathrm{_}$
$000$
$\mathrm{_}$ 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. $d\right)\frac{1}{12}$ Using long division method, $\mathrm{_}\mathrm{_}\mathrm{_}\left(\right)\underset{―}{0}.08\stackrel{―}{3}$
$12\right)100$
$-96$
$\mathrm{_}$
$40$
$-36$
$\mathrm{_}$
$04$
$\mathrm{_}$ 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.