How do you estimate percentages?

Question

Strangely, I haven't found a lot on that one on the internet (mostly videos clearly geared towards school children).

My issue: I am good at case math and good with numbers in general. Where I do have an issue - depending on the numbers - is to estimate a percent increase / decrease on the fly. This can be super useful to interpret a number quickly after you come up with it (and where it would sound ridicolous to take another 20 seconds to calculate it fully through in your head).

Ofc I know the typical tricks (i.e. if multiply the denominator close to 10 or 100 etc.) but sometimes I get really weird numbers, such as 37/587 where it is not really obvious at first. The only thing I could deduce here is tht it is between 5% and 10% (since 5% of 58 is 29 and 10% 58)

When I interview candidates I realize that flaw as well, i.e. most gravitate towards “it is a 50% percent decrease” even though when its much closer to 40%.

How do you handle that in general?

Answer 1

Let me suggest a different approach. You never know which one works best for you. This one requires you having a good grasp of the multiplication table.

1. 37/587 = 0,37 / 5,87 = 37% / 5,87

2. 37% / 5,87 → 37% / 6

3. 37% is pretty close to 36%

4. 36% / 6 = 6%

What I want to highlight here is that while you always want to round the denominator, doing the same on the numerator may not always be the best option. If you round up to 40 you are going to be less precise than “rounding” down to 36.

While 36 is not round… 36/6 is round! Much easier than 40/6

By the way, with this process you are likely to be more accurate than with rounding both numerator and denominator.

Having said this, both are acceptable during the interview. Use whatever works for you.

Answer 2

Hello,

I can suggest 2 methods that have worked for me:

1) Round both numbers

In your example of 37/587, I would round that to 40/600
This whole number fraction is a much more familiar number and easier to ‘memorize’ if need be
40/600 = 6.67%; 37/587 = 6.3%

2) Round the denominator and estimate multiples based on a fraction of that

So to take your example again, my thought process would have been: 37/587 is 37/600 → 1% of 600 is 6 → 6 * 6 is ~36 which is closest to 37, so the answer is ~6%

In both methods, its also useful to take note of the magnitude/direction that you round the numbers, that can affect the magnitude of error (though most often slightly).

Lastly, as an interviewer, if you had used method #1 and answered ~7% instead of 6.3%, i wouldn't really have cared. In terms of % and quant more generally, what I look out more for is

Order of magnitude errors → i.e. if the answer should be a clear single digit, and the candidate gives a double digit
Speed and accuracy of the actual calculation → i.e. if you come up with an answer quickly, and I ask you to explain how you came up with that number, it should match your formula

Other coaches may also suggest other useful methods that have worked for them. In the meantime, happy to answer any further questions on any of my points

Answer 3

Hi there,

It's really quite simple - you should round here (and confirm with the interviewer).

37/587 is like 40/600. That's like 20/300 which is like 10/150, which is like 1/15.

15 goes into 100 between 6 and 7 times (90 versus 105)…⅔ of the 15 is before the 100, so you're at 6.67%!

Answer 4

Hi there,

Two other things that you can try:

1. Rounding the number in the calculation e.g., 37/587 into 40/600, which makes it significantly easier.

2. Actually calculating the number :) Calculating it only takes a few seconds more and then you have the certainty that it's correct. Nobody expect you to be estimating and rounding all the time and often interviewers also see it as a sign of laziness.

Best,

Cristian