Question

Which of the following has a terminating decimal expansion? (a) 32/91 (b) 19/80 (c) 23/45 (d) 25/42

Answer 1

here ,


(a) $\frac{32}{91}$
91 = 7 × 13

(b)$\frac{19}{80}$
80 = 2 × 2 × 2 × 2 × 5

(c) $\frac{23}{45}$
45 = 3 × 3 × 5

(d) $\frac{25}{42}$
42 = 2 × 3 × 7

Since, 80 ends in ${2}^{4} \times {5}^{1}$

$\therefore{ \frac{19}{80} \: is \: a \: terminating \: decimal}$

Answer 2

Answer:

$\frac{19}{80}$

Step-by-step explanation:

To find whether given rational number is terminating decimal expansion or non-terminating repeating decimal expansion.

Step1:Do prime factors of numerator and denominator, if any

Step2: cancel any common factor ,if any

Step3: check that,if denominator has in the form

${2}^{n} {5}^{m} ; \: \: n ,\: m > 0$

if yes,then given number has terminating decimal expansion

otherwise not.

(a) 32/91

$\frac{2 \times 2 \times 2 \times 2 \times 2 }{7 \times 13} \\ \\ no \: common \: factor \: to \: cancel \\ \\ denominator \: is \: not \: in \: the \: form {2}^{n} {5}^{m} \\ \\ \frac{32}{91} : non - terminating \:$

(b) 19/80

$\frac{19}{80} = \frac{19}{ {2}^{4} \times5 } = terminating \: decimal$

(c) 23/45

$\frac{23}{45} = \frac{23}{3 \times 3 \times 5} = non - terminating$

(d) 25/42

$\frac{25}{42} = \frac{5 \times 5}{2 \times 3 \times 7} = non - terminating$

Hope it helps you.