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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}

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