Question

How do you calculate `(5.3times10^-2) times (-2.06times10^9)`?

Answer 1

-`1.0918 xx 10^8`

Explanation:

This is done in the same way as you would multiply in algebra.

`3x^5 xx -4x^-2`

This could be written as`(3 xx-4) xx (x^5 xx x^-2)`
Multiply the numbers,: `3 xx-4 = -12`
Multiply the variables by adding the indices.

`x^5 xx x^-2 = x^(5-2) = x^3`

`3x^5 xx -4x^-2 = -12x^3`

We can do the same with numbers in scientific notation:
`5.3 xx10^-2 xx -2.06 xx 10^9` can be written as:

`(5.3 xx -2.06) xx (10^-2 xx 10^9)`

Multiply the numbers,: `5.3 xx -2.06 = -10.918`

Multiply the powers by adding the indices.
`10^-2 xx 10^9 = 10^(-2+9) = 10^7`

`5.3 xx10^-2 xx -2.06 xx 10^9 = -10.918 xx 10^7`

However, in standard form there must be only one digit before the decimal point.
`-10.918 xx 10^7 = -1.0918 xx 10^8`