Which of the following is terminating decimal?

Foundation

Mathematics Foundation

HCF and LCM

Recurring Decimal Number

Linear Equations in One Variable

Question

Which of the following is terminating decimal? $\frac{23}{90}, \frac{111}{148}, \frac{29}{145}, \frac{1}{6}$

$\frac{1}{6}$

$\frac{23}{90}$

$\frac{111}{148}$

$\frac{29}{145}$

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Recall that in order for the decimal expansion of a fraction to terminate, the fraction's denominator, in fully reduced form, must have a prime factorization that consists of only 2's and/or 5's.

In fully reduced form, the denominator in A is 4 ,composed of only 2's, (4 = 2²).

In fully reduced form, the denominator in C is 5, composed of only 5's,(5 = 5¹) .

Hence, they have terminating decimals 0.75 and 0.2, respectively.

By contrast, the denominator in B has prime factors other than 2's and 5's (90 = 5 × 2 × x 3²),

and the fraction in D has the denominator 6, composed of prime factors other than 2's and 5's (6 = 2 × 3).

Therefore, options A and C are the correct answers.