Without actual division, show that the following rational number is non-terminating repeating decimal:

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Properties of Real Number

Recurring Decimal Number

Linear Equations in One Variable

Question

Without actual division, show that the following rational number is non-terminating repeating decimal: $\frac{129}{(2^{2} \times 5^{3} \times 7^{2})}$

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2,5 or 7 is not a factor of 129 so the fraction is in its simplest form. But for a rational number to be terminating decimal, its decimal should be in the form (2^m × 5ⁿ) but here the denominator is (2²× 5⁷× 7⁵) that is why given fraction is non -terminating repeating decimal.