How Percentages Are Used to Trick Us Every Day

I am 110% sure that you will enjoy this article.

The last statement is a lie, but not entirely for the reasons you think.

Obviously, I cannot be sure that you will enjoy reading this – I am not you, not everybody will like or be remotely interested in my writing, and indeed some of you will have stopped reading already.

But more significantly for what I want to talk about today, you cannot be 110% sure of anything.

I know that saying 110% or 150% are generally just figures of speech, exaggerations to make a point.

But I am equally concerned that percentages are all around us, and many of us do not really understand or appreciate what they really mean.

While you cannot be 110% sure of anything, your electricity bill can most certainly increase by 200% in a year and sadly may well have done recently.

Inflation falling from 10% a year to 4% a year does not mean that things are getting cheaper, but that they are getting more expensive more slowly.

This understanding gap on percentages can be easy for others to exploit, and we all need a basic knowledge of how this mathematical shorthand really works.

I can think of no better example than what is known as the potato paradox.

Imagine that I have 100kg of potatoes.

Aside from the fact that I will be eating a lot of chips, imagine too that those potatoes are 99% water, and 1% potatoness (the material other than water that makes potatoes what they are).

Most vegetables contain a lot of water, but that is not the key point here, so please do not worry about the nutritional value of potatoes.

Imagine now that I leave my potatoes in a sack overnight and they dry out a little.

The next day, they are only 98% water.

How much do my potatoes now weigh?

You may well answer 99kg.

Surely a 1% loss of water is 1% loss of the total weight.

But that is not how percentages work.

The answer is 50kg.

How can that possibly be true?

What has remained constant is the amount of potatoness present.

This was 1% of 100kg, so 1kg.

There is still 1kg of potatoness present the next day.

But this 1kg now represents 2% of the total weight of the potatoes, as they are now only 98% water.

If 1kg is 2%, then to get the total weight we multiply this by 50 to get to 100%, making the overall weight 50kg.

Shocking, isn’t it?

The trick here, aside from the fundamental lack of understanding of percentages that many of us have and that advertisers prey on constantly, is that what we should be focusing on is not the reduction in water from 99% to 98%, but the doubling in the percentage of potatoness from 1% to 2%.

It then makes a lot more sense that if that measure has doubled without any material change, then the overall weight must have halved.

But I did not talk about the 1% becoming 2%.

I just told you about the 99% reducing to 98%, which sounds totally insignificant.

Something doubling is a lot more alarming than something reducing from 99% to 98%, but in this case they are different sides of the same coin.

They both mean the same thing here.

If we can be that easily misled about a hypothetical bag of potatoes, what chance do we have with understanding mortgage rates or investment returns?

Percentages are a fundamental part of modern life.

Today you will see offers of 30% off, credit at 29.9% APR, mortgage rates fixed at 1.5% above base rate (which is also a percentage), and so on.

I do not pretend to understand all of these myself, especially the more complex financial calculations.

But I think that the key thing to remember is this.

Percentages are never an absolute value in themselves.

They are a measure of a proportion of something else.

We all understand that whether half a loaf of bread is enough for our lunch depends entirely on the size of the loaf of bread.

Every time we see the percentage sign, we should think the same way.

The percentage only means anything when we know exactly what it is being applied to.

It is just another way of writing a fraction.

But it is a lot easier to misuse to manipulate unwary consumers, like you and me.

So be on your guard 100% of the time, and when you are tempted by an offer involving percentages, remember my sack of potatoes!