Question

How do you simplify `(2.68×10^-5)×(4.40×10^-8)`?

Answer 1

`(2.68 xx 10^(-5)) xx (4.40 xx 10^(-8))`

`=(2.68 xx 4.40) xx (10^(-5) xx 10^(-8))`

`=11.792 xx 10^(-13)`

`=1.1792 xx 10^(-12)`

Explanation:

Note that `a^b * a^c = a^(b+c)`

So `10^(-5) xx 10^(-8) = 10^(-5+(-8)) = 10^(-13)`

When we multiply the mantissas `2.68 xx 4.40` the result is greater than `10`, so we divide it by `10` and adjust the exponent accordingly to give the result in scientific notation.