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

1 Answer
Feb 15, 2017

Answer:

#=-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