Question

Jada typically earns $1545 each month, of which $47.20 is spent on electricity. What percent of Jada's earnings are spent on electricity each month, to the nearest tenth of a percent?

Answer 1

`3.1%`

Explanation:

`color(blue)("Preamble about what percentage is")`

The % symbol is like a unit of measurement that is worth `1/100`
So for example: `50% ->50xx1/100 =50/100`

Percent is a fraction that has the bottom number (denominator) fixed at 100. So percent can be written as `" some number"%` or as `("some number")/100` They both represent the same thing.

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`color(blue)("Answering the question")`

Tenth is the first decimal place so you round off using the second decimal place as the guide for rounding up or rounding down.

As a fraction we have `("amount spent")/("earnings") -> 47.2/1545`

`color(brown)("Shortcut method")`

Divide the bottom number into the top number and then multiply by 100.

`47.2-:1545xx100" "=" "3.055..%` rounded this is `3.1%`

`color(white)(.)`

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`color(brown)("First principle method")`

Given: `47.2/1545`

We need to convert the bottom number into 100 and we can do this by multiplication using `100/1545`

For multiplication or divide, what we do to the bottom we also do to the top

`(color(white)(.)47.2xx100/1545 color(white)(.))/(1545xx100/1545)`

If you look at the top of this it is the same as the shortcut

`=(3.055....)/(100) " "=" "3.055xx1/100`

but `1/100` is the same as % so we write

`3.055...%`