Question

Without actually dividing find which of the following are terminating decimals.i. 3/25 ii. 11/18 iii. 13/20 iv. 41/42

Answer 1

Answer:

$\frac{3}{25}, \: and \: \frac{13}{20} \: are \\</p><p>terminating \:decimals$

Step-by-step explanation:

/* Let x = p/q be a rational number, such that the prime factorisation of q is of the form $2^{n}\times 5^{m}$,where n,m are non- negative

Integers .Then x has a decimal expansion which terminates. */

$i) Let \: x = \frac{3}{25}$

$q = 25 = 2^{0} \times 5^{2}$

$q\: is \: of \: the \: form \: 2^{n} \times 5^{m}$

Therefore,.

$x = \frac{3}{25} \: is \: terminating\: decimal$

$ii) Let \: x = \frac{11}{18}$

$q = 18 = 2^{1} \times 3^{2}$

$q\: is \: not \: of \: the \: form \: 2^{n} \times 5^{m}$

Therefore,.

$x = \frac{11}{18} \: is \: non-terminating,\\ repeating \: decimal$

$iii) Let \: x = \frac{13}{20}$

$q = 20 = 2^{2} \times 5^{1}$

$q\: is \: of \: the \: form \: 2^{n} \times 5^{m}$

Therefore,.

$x = \frac{13}{20} \: is \: terminating\: decimal$

$iv) Let \: x = \frac{41}{42}$

$q = 42 = 2^{1} \times 3\times 7$

$q\: is \:not \: of \: the \: form \: 2^{n} \times 5^{m}$

Therefore,.

$x = \frac{41}{42} \: is \: non-terminating\\ repeating \: decimal$

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Answer 2

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