Question

write the decimal expansion 13/125 , without actual division

Answer 1

13 /125 = 13 × 0.008


=0. 104

Answer 2

Hi friend, Harish here.

Here is your answer:

Given,

$An\ number= \frac{13}{125}$

To Find,

The decimal expansion of the given number without actual division.

Solution,

We know that,

$125 = 5\times 5\times 5 = 5^{3}$

So,

$\frac{13}{125} = \frac{13}{5^{3}}$

Now, Multiply ans divide the number by 2³.

Then,

$\frac{13}{5^{3}}= \frac{13}{5^{3}}\times \frac{2^{3}}{2^{3}} = \frac{13\times 8}{10^{3}}$

Here 5³ × 2³ = (5×2)³ = 10³   ( By using the identity)

So,

$\frac{13\times 8}{10^{3}} = \frac{104}{1000} = 0.104$

Therefore the value of the given number is 0.104.
_______________________________________________

Hope my answer is helpful to you.