Question

without actual division show that the following rational number is non terminating repeating decimal. 121/2^3*3^2*7^5

Answer 1

A non-terminating repeating decimal is a decimal number that continues endlessly, with no group of repeating digits.

A non-terminating repeating decimal cannot be represented as a fraction as a result are irrational numbers.

Given fraction,

121 / ( 2^3 * 3^2 * 7^5 )

= 11² / ( 2³ × 3² × 7⁵ )

as the factors of 11 are 1 and itself, so it cannot be divided by the terms present in the denominator.

As all the numbers are prime numbers and they do not cancel out each other, so it not a terminating decimal.

Hence it is a non-terminating repeating decimal.

Answer 2

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