Question

How do you express `(1.8*10^-2)-:(9*10^2)`?

Answer 1

See a solution process below:

Explanation:

First, we can rewrite this expression as:

`(1.8 * 10^-2)/(9 * 10^2)`

Next, we can rewrite this expression again as:

`(1.8/9) * ((10^-2)/(10^2))`

`0.2 * ((10^-2)/(10^2))`

Then, we can 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))`

`0.2 * (10^color(red)(-2)/10^color(blue)(2)) => 0.2 * 10^(color(red)(-2)-color(blue)(2)) => 0.2 * 10^-4`

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

`0.2 * 10^-4 => 2.0 * 10^-5`

If we want to express this in standard form we need to move the decimal point 5 places to the left because the 10s exponent is negative:

`2.0 * 10^-5 => 0.00002`