Question

write down the decimal expansion of 16/3125 without actual division

Answer 1

Hey siso !!

Here is your answer..

$= \frac{16}{3125} \\ \\ = \frac{16}{ {5}^{5} } \\ \\ = \frac{16}{ {5}^{5} } \times \frac{ {2}^{5} }{ {2}^{5} } \\ \\ = \frac{512}{100000} \\ \\ = 0.00512$


Hope it helps you...

Thanks..
^-^

Answer 2

Answer:

$\frac{16}{3125}=0.00512$  

Step-by-step explanation:

Given : Expression $\frac{16}{3125}$

To find : Write down the decimal expansion of expression without actual division?

Solution :

We can factories the numerator and denominator then if the denominator is in the form $2^m\times 5^m$ then m is the number of decimal place.

Now, Let $x=\frac{16}{3125}$

$x= \frac{16}{3125}\\\\x=\frac{16}{ {5}^{5}}\\\\x=\frac{16}{{5}^{5}}\times\frac{{2}^{5}}{{2}^{5}}\\\\x=\frac{512}{100000}\\\\ x=0.00512$

as m = 5 so the decimal expansion is after 5 decimal places.

Therefore, $\frac{16}{3125}=0.00512$