MHB Improving Interpretation of Percentages: Tips and Examples

[Erik1]

I know how to work out percentages but I would like to get better at interpreting their significance. Has anyone got any suggestions/examples? Thanks

 

[Nono713]

What kind of significance are you looking for? Essentially a "percentage" literally means "per cent" or, in other words, "parts per hundred". So a percentage of 77% means, 77 parts in a hundred, or a proportion of 77/100 = 0.77. Formally, "%" is equivalent to "divided by 100", as the symbol stands for "per cent" where "cent" stands for 100 (probably comes from the French "cent" which means "a hundred", but I wouldn't know).

So the symbol is a useful shortcut when you want to denote proportions in a way that's more suitable for display, since "0.77" doesn't ring bells for the less mathematically inclined people, whereas 77% immediately tells them that some quantity exists in 77 parts in a hundred of another (that is the ratio interpretation, which I guess is what percentages are usually for).

If that makes any sense

 

[Farmtalk]

Bacterius provided a great analysis of what percentages mean. Here are a couple of examples that I found useful to go with it.

If your local weather man says today is going to be partly cloudy with a 20% chance of rain, you know that there is a small likelihood for you to get wet today. In fact, there is a 20/100 chance, or 1/5 chance that you will get wet; not high odds.

If the next day, your local weather man says today is going to be mostly cloudy with a 80% chance of rain in the afternoon, you know there is a large likelihood for you to get wet today. That would be an 80/100 chance, or 4/5 chance that you will get wet; better bring an umbrella.

Also, if you go to your department store, and see that there is a new television with a sticker tag of 799 dollars but it is 40% off, then you know your going to save a lot of money because 40/100 of that price is free, so you only have to pay 60/100 or 60% (About 479 dollars).

Hope this helps! If not, please elaborate on what you're wanting exactly.(Cool)

 

[Erik1]

I especially struggle to analyse percentage increases/ decreases. Sorry for not putting more information initally.

 

[Farmtalk]

Ok, well let's say that Save-a-Lot currently sells a 1 gallon jug of 2% milk for 2.99 but due to the rough economy, has to rise their price to 3.69 (Hypothetical situation). What is the percentage increase of the price?

What you could do, and what I do, is subtract the new price from the original price, (3.69-2.99= 0.70), and then divide that number by the new number (Which is 3.69) and multiply by 100 to get your percentage difference:

$$3.69-2.99= 0.70$$

$$\frac{0.70}{3.69}= 0.18970...$$

$$0.18970...*100 = 18.970$$ percent

We multiply by 100 because we are going from decimal to percentage form.

Does this make sense?

 

[MarkFL]

Ok, well let's say that Save-a-Lot currently sells a 1 gallon jug of 2% milk for 2.99 but due to the rough economy, has to rise their price to 3.69 (Hypothetical situation). What is the percentage increase of the price?

What you could do, and what I do, is subtract the new price from the original price, (3.69-2.99= 0.70), and then divide that number by the new number (Which is 3.69) and multiply by 100 to get your percentage difference:

$$3.69-2.99= 0.70$$

$$\frac{0.70}{3.69}= 0.18970...$$

$$0.18970...*100 = 18.970$$ percent

We multiply by 100 because we are going from decimal to percentage form.

Does this make sense?

If we wish to find the percentage of increase in the price, we actually want to take the increase and divide it by the original price, then multiply by 100. We are in essence, wanting to know what we need to multiply the original price by to get the new price. If $p$ is the percentage increase, then we could state:

$$\left(1+\frac{p}{100} \right)2.99=3.69$$

Now, solving for $p$, we find:

$$1+\frac{p}{100}=\frac{3.69}{2.99}$$

$$\frac{p}{100}=\frac{3.69}{2.99}-1=\frac{3.69-2.99}{2.99}$$

$$p=\frac{3.69-2.99}{2.99}\cdot100$$

 

[Farmtalk]

You are correct, I will delete my original comment so I don't provide false information. Sorry for this. (Blush)

 

[MarkFL]

You are correct, I will delete my original comment so I don't provide false information. Sorry for this. (Blush)

No need to delete your original comment...in fact it can be helpful as many people aren't sure with which quantity to divide the change by to find the percentage change. :D

I know some students are confused by the fact that for example if they increase a quantity by 20%, why they can't decrease the new quantity by 20% and get back to the original quantity, and it is because of the fact that the 20% is taken from two different quantities.

 

[Farmtalk]

That makes sense! I appreciate the clarification! This thread turned out pretty important for more than one user!:D