Question

How do you calculate `(2.16times10^2) / (3times10^-4)`?

Answer 1

It is `720,000`.

Explanation:

You can arrange your equation first:

`216/0.0003`

`=(216times10^4)/3`

`72times10^4`

or

`720,000`

This is your answer

`720,000`

Answer 2

divide the digits and then adjust the exponents

Explanation:

`2.16/3 = 0.720`

`0.72 = 7.20 xx 10 ^-1`

`(10^-1 xx 10^2) / 10^-4 = 10^1/10^-4 = 10^5`

the answer is `7.20 xx 10^5`

Answer 3

See a solution process below:

Explanation:

First, rewrite this expression as:

`(2.16/3) xx (10^2/10^-4) => 0.72 xx 10^2/10^-4`

Now, use this rule of exponents to calculate the 10s terms:

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

`0.72 xx 10^color(red)(2)/10^color(blue)(-4) => 0.72 xx 10^(color(red)(2)-color(blue)(-4)) => 0.72 xx 10^(color(red)(2)+color(blue)(4)) =>`

`0.72 xx 10^6`

To write this in proper scientific notation we need to move the decimal point 1 place to the right so we must subtract `1` from 10s exponent:

`0.72 xx 10^6 => 7.2 xx 10^5`