# Without Actually Performing the Long Division,129 2 2 × 5 7 × 7 17 - Mathematics

Numerical

Without actually performing the long division, state whether state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

$\frac{129}{2^2 \times 5^7 \times 7^{17}}$

#### Solution

The given number is $\frac{129}{2^2 \times 5^7 \times 7^{17}}$

Clearly, none of 2, 5 and 7 is a factor of 129.

So, the given number is in its simplest form.

Now,

$2^2 \times 5^7 \times 7^{17}$  is not of the form
$2^m \times 5^n$
So, the given number has a non-terminating repeating decimal expansion.
Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 1 Real Numbers
Exercise 1.6 | Q 1.5 | Page 56