# Simple math question, will help me at work

1. Nov 11, 2012

### SimpleSoCal

So my white collar job demands lots of number crunching as of lately. Now this is most likely simple, and I guess I should know this but.... here it goes.

I just need to know how to calculate a percentage difference on the calculator.

For example. I take 1.46 * .28 which equals .4088. I then take 2.47 * .5 which obviously halves it to 1.235.

I know how to find percentages, like a simple X * whatever percent I want. What I'm asking is, what simple thing would I do on the calculator to get the percentage difference between .4088 and 1.235?

2. Nov 11, 2012

### chiro

Hey SimpleSoCal.

If you want to find how much larger one thing is in terms of another then you need to look at the ratio of the two objects.

For example with your numbers, the ratio of the two numbers 0.4088/1.235 = 0.3310121 and the difference between the two is found by subtracting 1 from the answer which gives -0.6689879 or in other words 0.4088 is -66.89879% larger than 1.235.

Now if you reverse the order you get 1.235/0.4088 = 3.021037 and minus 1 gives 2.021037 or 1.235 is 202.1037% larger than 0.4088.

You can interpret negative numbers like -66.89879% to be 66.89879% smaller than the larger value (so if you talk about the positive % then you are talking about much smaller something is).

If two things are equal then the ratio of both is equal to 1 and 1-1 = 0 which is a 0% difference which is what we expect.

3. Nov 11, 2012

### LeonhardEuler

It depends what you want the difference as a percentage of. 1.235 - 0.4088 = 0.8262. If you want the difference as a percentage of 1.235, it is
$$100*\frac{0.8262}{1.235} = 66.9\%$$
If you want the difference as a percentage of 0.4088, it is
$$100*\frac{0.8262}{0.4088} = 202.1\%$$
And similarly to get the difference as a percentage of any other number.

4. Nov 11, 2012

### SimpleSoCal

Thanks, guys! That helps tons. I hope I made sense on my end. What I really meant to say was percentage increase I guess. Like how much more percent bigger is 1.235 than .4088

5. Nov 11, 2012

### chiro

You'll want to use the formula I posted in that case.

Remember that an increase or decrease means you have to subtract 100% from the answer which just means subtracting 1.

6. Nov 11, 2012

### SimpleSoCal

Gotcha. Man, this place is great. More than I need but it's all useful. Thank God for the internet.