Question

How do you simplify `\frac { 0.9\times 10^ { - 2} } { 9\times 10^ { - 8} }`?

Answer 1

See a solution process below:

Explanation:

First, rewrite the expression as:

`0.9/9 xx 10^-2/10^-8 => 0.1 xx 10^-2/10^-8`

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

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

`0.1 xx 10^color(red)(-2)/10^color(blue)(-8) => 0.1 xx 10^(color(red)(-2)-color(blue)(-8)) => 0.1 xx 10^(color(red)(-2)+color(blue)(8)) =>`

`0.1 xx 10^6`

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

`0.1 xx 10^6 => 1 xx 10^5`