# The market bought grapes for $0.87 a pound and sold them for$1.09 a pound. What is the percent of increase rounded to the nearest tenth?

Oct 27, 2016

Unless told otherwise the increase will be compared to the original value. So we are comparing to $0.87 Increase is the change which is $1.09-$0.87 =$0.22

So expressed as a fraction the change is ($0.22)/($0.87)

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$\textcolor{b l u e}{\text{Using the shortcut method}}$

The percentage change is: (0.22-:0.87)xx100= 25.28735...%

Rounded to the nearest tenth 25.3% to 1 decimal place

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$\textcolor{b l u e}{\text{Using first principle method}}$

A percentage in fraction form is $\frac{\text{some number}}{100}$

So we need to change ($0.22)/($0.87) such that the bottom number (denominator) is 100.

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So we need to manipulate $0.87 this way: $0.87 \times \frac{100}{0.87}$is the same as $\text{ "0.87/0.87xx100" " =} 2 1 \times 100$To maintain the correct ratio what we do to the bottom we also do to the top. ....................................................................................... Multiply top and bottom by $\frac{100}{0.87}$giving: $\frac{0.22 \times \frac{100}{0.87}}{0.87 \times \frac{100}{0.87}} \leftarrow \text{the top is the same as the shortcut}$giving $\text{ } \frac{25.28735 \ldots}{100}$which is the same as 25.3% to 1 decimal place. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ $\textcolor{p u r p \le}{\text{Footnote}}$$\textcolor{p u r p \le}{\text{Did you know that "%" is really a unit of measurement}}$In the same way that centimetre is the unit size of " "(1" metre")/100 %  is the unit size of $\frac{1}{100}\$ of something.

So for example 60% -> 60/100 of something