# How do you evaluate \frac { 5\times 10^ { 7} } { 25\times 10^ { 4} }? What is the answer in scientific notation?

Mar 21, 2017

$\frac{5 \times {10}^{7}}{25 \times {10}^{4}} = 2 \times {10}^{2}$

#### Explanation:

In scientific notation, we write a number so that it has single digit to the left of decimal sign and is multiplied by an integer power of $10$.

For example here we have $5 \times {10}^{7}$ in numerator and $25 \times {10}^{4}$ in denominator.

While dividing first by second, we can use the identity ${a}^{m} / {a}^{n} = {a}^{\left(m - n\right)}$ and doing this we get

$\frac{5 \times {10}^{7}}{25 \times {10}^{4}}$

= $\frac{5}{25} \times {10}^{\left(7 - 4\right)}$

= $\frac{1}{5} \times {10}^{3}$

= $0.2 \times {10}^{\left(7 - 4\right)}$

Now here we have first digit $2$ in one-tenth place and not in unit's place as desired for scientific notation. Hence, we put $0.2$ as $\frac{2}{10}$ and this gives us

$\frac{5 \times {10}^{7}}{25 \times {10}^{4}} = \frac{2}{10} \times {10}^{3} = 2 \times {10}^{2}$