Question

How do you simplify `(1.032times10^-4)/(8.6times10^-5)`?

Answer 1

See a solution process below:

Explanation:

First, rewrite this expression as:

`(1.032/8.6) xx (10^-4/10^-5) => 0.12 xx (10^-4/10^-5)`

Next, use this rule of exponents to simplify the 10s term:

`x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))`

`0.12 xx (10^color(red)(-4)/10^color(blue)(-5)) => 0.12 xx 10^(color(red)(-4)-color(blue)(-5)) => 0.12 xx 10^(color(red)(-4)+color(blue)(5)) =>`

`0.12 xx 10^1`

If we want this in true scientific notation form we need to move the decimal point one place to the right which means we need to subtract `1` from the 10s exponent:

`0.12 xx 10^1 => 1.2 xx 10^0`

If we want this in standard form it is:

`1.2 xx 10^0 => 1.2 xx 1 => 1.2`