Question

How do you simplify `(8.4\cdot 10^ { 4} ) + ( 1.7\cdot 10^ { 4} )`?

Answer 1

`1.01xx10^5`

`color(brown)("Shown in a lot of detail so you can see what is happening.")`
`color(brown)("Once you get used to these you will do a lot of it in your head.")`

Explanation:

Notice that `10^4` is common ( it is in both brackets)

Factor out the `10^4` giving:

`10^4(8.4+1.7)`

`10^4(10.1) " "=" "10.1xx10^4`

But this is not in the same format as in the question.

Multiply 10.1 by 1 but in the form of `1=10/10`

`color(green)([10.1color(red)(xx1)]xx10^4" "->" "[10.1color(red)(xx10/10)]xx10^4 )`

`" "color(green)([10.1/(color(red)(10))color(red)(xx10)]xx10^4)`

`" "1.01xx10color(white)(.)xx10^4`

`" "=" "1.01xx10^5`