# 200% of the number vs improvement by 200%

I suck at maths, so this is probably a really stupid elementary question, but here it goes. 0.5 out of 1 is 50%, 1 out of 1 is 100%, 2 out of one is 200%,etc. So if that’s the case, 7 out of 1 is 700%, but, if something goes from a 1 to a 7, is that a 700% improvement or a 350% improvement?

In 3d modeling, Photoshop,etc. when you scale something by a 100%, you don’t do anything, you remain at “1 out of 1”, so by that logic a 7x improvement is 700%, however in real life people consider something that is “100% times better” to be twice as better, so 2 out of 1 in this case or 350% in the case of the seven, so which one is it?

If something goes from 1 to 7, it’s a 600% improvement.

For blatant innumeracy, come to Thailand. A jewelry store selling gems at ⅓ the marked price described this as a “300% discount.” Oh — and when buying 18 karat gold make sure you ask whether these are Thai karats or Western karats. (This may be why Thais buy only 24 karat gold; 24 karats is the same in any base.)

When the baht-dollar ratio fell from 26 to 39, the Bangkok Post announced that the baht had “lost half its value.” The ratio eventually did go to 52, but the Post was inconsistent and didn’t write then that the baht had “lost all its value.”

Innumeracy is pretty common around the world. A few weeks ago I went into a shop to buy something that was discounted at 20%. They were also offering an additional 20% on selected items and this was one of them.

At the checkout, the assistant added 20 and 20 and knocked 40% off. I was pretty happy with that as he had given me an extra 4%. Okay, it was only £2.00 but it made me feel superior

Going from 1 to 7 is the same as going from 100% to 700%, which is an increase of 600%.

Saying “100% better” means increasing from 100% to 200%, which is the same as going from 1 to 2.

However, people sometimes say “100% better” meaning a decrease of something bad (e.g. “My poison ivy rash is 100% better!”). So, in that situation, it’s a decrease from 100% to 0%, which is the same as going from 1 to 0.

Consider that there’s such a thing as a “10% increase”. What does that mean? Clearly it doesn’t mean that the new value is 10% of the old one: That’s not an increase. What it means is that the increase is 10% of the old value. If your old pay was \$9.50 an hour, and it’s increased by 10%, then that means that you’re getting a raise of \$0.95, bringing your total pay to \$10.45 .

Likewise, if you were to get a 600% increase in your pay, that would mean that the increase was 600%, and so your new total pay would be your original pay plus six times your original pay, for a total of 7 times what it was.

And the new value is 700% of the old value. It’s just a matter of how you want to say it and how much hype you need. Let’s say a stock price rises to twice yesterday’s price. Which headline are you going to write:

Stock increases by 100%
Stock value now 200% of yesterday’s close
Stock value doubled

The interesting thing is that if the price increases by 100%, and then falls by 50%, you’re back to where you started.

Similarly nine flat years and one with 10% growth is equivalent to 0.96% annual growth. I’ll guess that many get this calculation wrong.

Is there evidence that false advertising of store sales is more due to innumeracy rather than blatant lies? Has anyone successfully complained because they got 0% off instead of “100% off” or whatever the misleading advertisement literally said?

I think there are two issues here.

One thing that trips people up when it comes to percents is that it matters, often a great deal, what the base rate is—that is, what it’s a percent of. This is why things like this

that look paradoxical are perfectly correct.

The other issue is that there’s confusion and ambiguity in the way people use phrases like “X times more” in everyday speech, as discussed in threads like this one: Is “X times as much” the same as “X times more”? (Or worse, “Three Times Less Than.”)

I also one time bought a 3 liter bottle of soda that on the proclaimed on its side that it contained “33% more than a 2 liter bottle!”

I’ve often seen advertisers work innumeracy into their product advertising, but usually they don’t do it in such a way as to reduce the significance of their claims.