Question

How do you evaluate `(5.18times10^2)(9.1times10^-5)`?

Answer 1

`0.047138`

Explanation:

`(5.18 xx 10^2)(9.1 xx 10^-5)`

`:.a^-5=1/a^5`

`:.=(5.18 xx 100)(9.1/10^5)`

`:.=518 xx 9.1/100000`

`:.=518 xx 0.00091`

`:.=0.047138`

Answer 2

`4.7138xx10^(-2)`

Explanation:

Lets get rid of all the decimal places and put them back at the end.

`5.18xx10^2=518`

`9.1xx10^(-5)=91xx10^(-6)`

So now we have: `518xx91xx10^(-6) larr" "10^(-6)" is the same as "1/10^6`

For the moment disregard the `10^(-6)`

`color(white)(00)518`
`ul(color(white)(000)91)larr" Multiply"`
`color(white)(0)4662larr 518xx90`
`ul(color(white)(00)518)larr 518xx1`
`47138 larr 4662+518`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Now we put back the `xx1/10^6`

`47138xx1/10^6" "=" "0.047138`

Writing this in the same format as in the question (a good move)

`4.7138xx1/10^2" "->" " 4.7138xx10^(-2)`