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}

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, $0.1\bar{3}$
$,1520$
$-15$
$\mathrm{\_}$
$050$
$-45$
$\mathrm{\_}$
$05$ 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. $b)\frac{11}{20}$ Using long division method, $\mathrm{\_}\mathrm{\_}\mathrm{\_}()\underset{―}{0}.55$
$20)110$
$-100$
$\mathrm{\_}$
$0100$
$-100$
$\mathrm{\_}$
$000$
$\mathrm{\_}$ 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. $c)\frac{17}{40}$ Using long division method, $\mathrm{\_}\mathrm{\_}\mathrm{\_}()\underset{―}{0.}425$
$40)170$
$-160$
$\mathrm{\_}$
$0100$
$-80$
$\mathrm{\_}$
$200$
$-200$
$\mathrm{\_}$
$000$
$\mathrm{\_}$ 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. $d)\frac{1}{12}$ Using long division method, $\mathrm{\_}\mathrm{\_}\mathrm{\_}()\underset{―}{0}.08\bar{3}$
$12)100$
$-96$
$\mathrm{\_}$
$40$
$-36$
$\mathrm{\_}$
$04$
$\mathrm{\_}$ 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.