Question

24/980 terminating decimals or non termination

Answer 1

Question :- 24/980 terminating decimals or non termination ?

Concept used :-

• we have to check prime factors of denominators of given fraction .
• if Prime factor are 2, or 5 , or 2 and 5 both . Than the given fraction is a terminating decimal expansion .
• if prime factors are other than 2 or 5 , than the given fraction is a non - terminating decimal expansion .

Solution :-

Denominator of the given fraction is 980.

So,

Prime factors of 980 are :-

→ 980 = 2 * 2 * 5 * 7 * 7

As we can see we have both factors 2 and 5 but also have a prime factor 7.

Therefore, by above told concept , if prime factors are other than 2 or 5 , than the given fraction is a non - terminating decimal expansion .

Hence, (24/980) is a non terminating decimal expansion.

Answer 2

$Given \: rational \:number \: \frac{24}{980}$

Prime Factorisation of 24 and 980:

24 = 2 × 2 × 2 × 3

980 = 2 × 2 × 5 × 7 × 7

$= \frac{2\times 2 \times 2 \times 3 }{ 2\times 2 \times 5 \times 7 \times 7 }$

/* After cancellation ,we get */

$= \frac{2 \times 3 }{ 5 \times 7 \times 7 }$

$= \frac{6}{5\times 7^{2} }\: \blue{ ( Least \: form )}$

$\green {= Non \: terminating \: decimal }$

$\underline {\red{ Reason: }}$

$\pink{ (Denominator \: is \: not \: of \: the }$

$\pink{ form\: 2^{n} \times 5^{m}) }$

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