Question

How do you find the percent change if original: $3.78 and new: $2.50?

Answer 1

`=-33.862`% to 3 decimal places

Full 'teach in' given about percentages

Explanation:

`color(blue)("Preamble")`

In percentage the symbol % may be viewed as a unit of measurement that is worth `1/100`

As and example `60%` is the same as `60xx1/100=60/100`

In this type of question it is usual to express the change using the original value is the reference point. Expressed as a fraction we have:

`("change")/("reference point value") -> ("changed value- original value")/("original value")`

If changed value - original value is negative then it indicates a reduction. As is the case in this question.
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`color(blue)("Answering the question")`

`color(brown)("Starting point:")`

`("changed value- original value")/("original value") -> ($2.50-$3.78)/($3.78)`

`=-($1.28)/($3.78)`

By the way; like in numbers the $ symbols cancel out in the same way numbers do. This is a useful trick when doing higher mathematics or physics

So we have `(-cancel($)1.28)/(cancel($)3.78) = -1.28/3.78`

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`color(brown)("Converting this into percentage")`

Remember that `1/100->%`

`color(green)((1.25)/(3.78)color(red)(xx1)" "->" "(1.25/3.78color(red)(xx100/100))`

`(-1.28/3.78color(red)(xx100xx1/100))`

`(-1.28/3.78color(red)(xx100xx%))`

`(-1.28/3.78color(red)(xx100))%`

`=-33.862`% to 3 decimal places