Question

How do you simplify `(4.65times10^-2)(5times10^6)`?

Answer 1

`2.325xx10^5`

Explanation:

This is just one of several tricks. To multiply a decimal by 10 is strait forward. So lets see if we can incorporate that.

Not that 5 is the same as `10xx 1/2`

`color(blue)("Just dealing with the numbers")`

`4.65xx5 color(white)("ddd")->color(white)("ddd")4.65xx10xx1/2`

`color(white)("ddddddddd")->color(white)("ddd")46.5xx1/2`

`color(white)("ddddddddd")->color(white)("ddd") 23.25`

`color(white)("ddddddddd")->color(white)("ddd"color(green)(2.325xx10)`

There should only be one digit to the left of the decimal point and it is not 'allowed' to be 0.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Just dealing with the 10's part of "(4.65xx10^(-2))(5xxxx10^6))`

Believe it or not all we have to do is add the indeces

`10^(-2)xx10^6color(white)("d")=color(white)("d")10^(6-2)color(white)("d")=color(white)("d")color(green)(10^4)`
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`color(blue)("Putting it all together")`

`color(green)(2.325xx10xx10^4)`

This may be written as:

`2.325xx10^1xx10^4`

`2.325xx10^(1+4)`

`2.325xx10^5`