Question

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

Answer 1

`(0.4xx10^(-6))(0.7xx10^-2)=2.8xx10^(-9)`

Explanation:

`(0.4xx10^(-6))(0.7xx10^-2)`

= `0.4xx10^(-6)xx0.7xx10^-2`

= `0.4xx0.7xx10^(-6)xx10^-2`

= `4/10xx7/10xx10^((-6)+(-2))`

= `28/100xx10^(-8)`

= `0.28xx10^(-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 `(0.4xx10^(-6))(0.7xx10^-2)=2.8xx10^(-1)xx10^(-8)=2.8xx10^(-9)`