# How do you simplify (0.4 times 10^-6)(0.7 times 10^-2) and write the answer in scientific notation?

Jul 3, 2016

$\left(0.4 \times {10}^{- 6}\right) \left(0.7 \times {10}^{-} 2\right) = 2.8 \times {10}^{- 9}$

#### Explanation:

$\left(0.4 \times {10}^{- 6}\right) \left(0.7 \times {10}^{-} 2\right)$

= $0.4 \times {10}^{- 6} \times 0.7 \times {10}^{-} 2$

= $0.4 \times 0.7 \times {10}^{- 6} \times {10}^{-} 2$

= $\frac{4}{10} \times \frac{7}{10} \times {10}^{\left(- 6\right) + \left(- 2\right)}$

= $\frac{28}{100} \times {10}^{- 8}$

= $0.28 \times {10}^{- 8}$

Now to right the result in scientific notation, we need to shift decimal in $0.28$, one point to right (to make only one digit to left of decimal point), i.e. multiply by $10$ and hence we should also multiply it by ${10}^{- 1}$.

Hence $\left(0.4 \times {10}^{- 6}\right) \left(0.7 \times {10}^{-} 2\right) = 2.8 \times {10}^{- 1} \times {10}^{- 8} = 2.8 \times {10}^{- 9}$