Question

Write down the decimal expansion of the following
rational numbers by writing their denominators in
the form of 2^m× 5^n; where m and n are nonnegative integers.
(i)77/1120
(ii)441/288

Answer 1

Answer:

1) 77 / 1120

ans

take the hcf of 77 and 1120 by prime factorisation

so

77 = 7 × 11

1120 = 2^5 × 7^1 × 5^1

for finding the result

we have to see always denominator

so

it is not in the forn of 2^m × 5^n

hence it is non terminating repeating decimal

2)

441 / 288

ans

take the hcf of 441 and 288

441 = 3^2 × 7 ^2

288 = 2^5 × 3^2

for finding the result

we have to see always denominator

so

it is not in the forn of 2^m × 5^n

hence it is non terminating repeating decimal

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Answer 2

Answer:

1)77/1120

solution -

take the HCF of 77 and I 120 by Prime factorization

so

77 =7 * 11

1120=2^5 * 7^1 * 5^1

for finding the result

we have to see always

denominator so

it is not in the form of2^m * 5^n

hence it is not terminating repeating decimal.

2)441/288

solution -

take the HCF of 441 and 288

441=3^2 * 7^2

288=2^5 * 3^2

for finding the result

we have to see always denominator so

it is not in the form of 2^m * 5^n.

hence it is non terminating repeating decimal.

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