# How to simplify (6.3 times 10^5) ÷ (9 times 10^3) in scientific notation?

Mar 18, 2018

$7.0 \times 10$

#### Explanation:

$6.3 \times {10}^{5}$ is the same value as $63 \times {10}^{4}$

So we have:

$\frac{63 \times {10}^{4}}{9 \times {10}^{3}} \textcolor{w h i t e}{\text{ddd") -> color(white)("ddd}} \frac{63}{9} \times {10}^{4} / {10}^{3}$

$\textcolor{w h i t e}{\text{ddddddddd.d")->color(white)("ddd}} \frac{63}{9} \times 10$

If the sum of the digits is exactly divisible by 3 then the actual number is also exactly divisible by 3 $\to 6 + 3 = 9$ so we will divide both top and bottom by 3 to simplify the fraction.

$\textcolor{w h i t e}{\text{ddddddddd.d")->color(white)("ddd}} \frac{63 \div 3}{9 \div 3} \times 10$

Note that:

$\frac{63 \div 3}{9 \div 3} = \frac{21 \div 3}{3 \div 3} = \frac{7}{1} = 7$ so we have:

$\left(6.3 \times {10}^{5}\right) \div \left(9 \times {10}^{3}\right) = 7.0 \times 10$