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

Feb 15, 2017

$= - 33.862$% to 3 decimal places

Full 'teach in' given about percentages

#### Explanation:

$\textcolor{b l u e}{\text{Preamble}}$

In percentage the symbol % may be viewed as a unit of measurement that is worth $\frac{1}{100}$

As and example 60%  is the same as $60 \times \frac{1}{100} = \frac{60}{100}$

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:

$\left(\text{change")/("reference point value") -> ("changed value- original value")/("original value}\right)$

If changed value - original value is negative then it indicates a reduction. As is the case in this question.
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$\textcolor{b l u e}{\text{Answering the question}}$

$\textcolor{b r o w n}{\text{Starting point:}}$

("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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$\textcolor{b r o w n}{\text{Converting this into percentage}}$

Remember that 1/100->%

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

$\left(- \frac{1.28}{3.78} \textcolor{red}{\times 100 \times \frac{1}{100}}\right)$

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

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

$= - 33.862$% to 3 decimal places