Question

Write the decimal expansion of 16/3125 without actual division

Answer 1

Decimal expansion of  $\bold{\frac{16}{3125}}$  is 0.00512.

Solution:

To find the actual answer without division we need to write the number in their power form that is for $16=2^{4} \text { and } 3125=5^{5}$

$\frac{16}{3125}=\frac{(2 \times 2 \times 2 \times 2)}{(5 \times 5 \times 5 \times 5 \times 5)}$

                               Or

$\frac{16}{3125}$ can also be written as the below form,

$\frac{16}{3125}=\frac{16 \times 2 \times 2 \times 2 \times 2}{(10 \times 10 \times 10 \times 10 \times 10)}$

In the second part, the denominator 10 can be reduced to 5 by the value 2 in the numerator which gives the given value.

Using the second part, we get $\frac{16 \times 2 \times 2 \times 2 \times 2}{(10 \times 10 \times 10 \times 10 \times 10)}= \bold{\frac{256}{100000}=0.00256}$

Answer 2

Answer:

$Decimal \:form \:of \:\frac{16}{3125}=0.00512$

Step-by-step explanation:

$Given \: \frac{16}{3125}\\=\frac{2^{4}}{5^{5}}\\=\frac{2^{4}\times 2^{5}}{5^{5}\times 2^{5}}\\=\frac{2^{4+5}}{(5\times 2)^{5}}\\=\frac{512}{10^{5}}\\=\frac{512}{100000}\\=0.00512$

Therefore,

$Decimal \:form \:of \:\frac{16}{3125}=0.00512$

•••♪