# How do you find the percent change if original: 124 tons and new: 137 tons?

Nov 10, 2015

10.58387 % I have also explained why people say "multiply by 100".

#### Explanation:

The use of the word 'change' indicates that the obtained figure is compared against is the original weight. Change is 'difference' so we have:

$\textcolor{b l u e}{\text{difference is 137 - 124 = 13 tons.}}$
$\textcolor{b r o w n}{\text{Always remember to use the units of measurement.}}$ It is good practice, gains you marks and becomes very important when dealing with more complex calculations.

We need to compare this against something so we use the original weight. That is, a proportion of the original weight expressed as

$\textcolor{w h i t e}{\times \times \times \times} \frac{13}{124}$. This is 13 for 124 parts!

color(green)(.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~)

$\textcolor{b l u e}{\text{I am now going to show you something really cool!!!}}$
But this is a ratio comparing to 124 parts. We need the ratio compared to 100 parts. So I am now going to show you $\textcolor{red}{\text{why}}$ people say multiply by 100. $\textcolor{b r o w n}{\text{A number of people will only know this as a shortcut without}}$
$\textcolor{b r o w n}{\text{fully understanding what it is actually doing.}}$

If we do this: $\text{ "(13 divide 124)/(124 divide 124) = (0.1048387....)/1 "for 1 part}$

That is:$\textcolor{w h i t e}{\times \times \times \times \times \times} \left(0.1048387 \ldots \text{parts".)/(1 " part}\right)$

But we need 'for 100 parts. So we now do this:

(0.1048387....times 100)/(1 times 100) = (10.48387..)/100 =10.58387 %

which is to 5 decimal places ( 5dp).

color(green)(.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~)
$\textcolor{red}{\text{Shortcut method}}$

color(red)( 13/124 times 100 = 10.584 %color(white)(xxxx) to 3dp