Math tricks for small decimal numbers

Jana asked on Sep 06, 2017 - 5 answers
Currently preparing for BCG interview.

Hello together,

I'm wondering if anybody might have a nice trick for me to deal with divisions with small numbers. For example I'm struggeling with cases like this : 0.024 / 0.8 = ?

Of course I can directly see that it must be something with 3 and if I do the long way of expanding the 0.024 to a bigger number I come to the right conclusion of 0.03. However, it simply takes me too much time. For multiplications with large numbers I do the trick with x 10^n and with that I'm really fast.

Maybe someone knows a nice way to 1.) avoid mistakes with the zeros after the comma and 2.) to speed up the calculation.

Thanks a lot in advance!



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Anonymous A replied on Sep 07, 2017

Hi Jana,

It won't work where you have really ugly numbers but one trick to keep in mind is the 'invert and multiply'.

So to use your case:

0.024/0.08 = (0.024/1) / (4/5)

= 0.024 * 5 / 4

= 0.12 / 4

= 0.03

Its also useful if you have numbers which can be expressed as fractions in both the numerator and denominator:

e.g. 0.33 / 0.2

= (1/3) / (1/5)

= (1/3) * (5 /1)

= 5/3

= 1.67

replied on Sep 11, 2017
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Basically, it's about 2 skills:

1) Learn how to work with zeros. You've mentioned - always use 10^power instead of zeros


300x9000 = 3*10ˆ2 x 9*10ˆ3=3x9*10ˆ(2+3)=27*10ˆ5

Handwritten it looks not that complicated. If you get used to writing all the numbers that way, you will never loose zeros and all multiplications/divisions will be replaced with + or -.

2) Learn the division table up to 1/11 (i.e. 5/6 = 83.3%). It will help you calculate any percentage problems

p.s. Use math tools(Mimir math for iOS, Math tool on Viktor Cheng website) to practice. Train, train, and train again

Matteo replied on Sep 09, 2017
Preparing for interviews in autumn

Hi, if you are already quick and comfortable using the 10^n for big numbers, you can use the same exact trick for decimal numbers, but remembering to use the -n to actually "reduce" the number; so in your case 0.024 = 24* 10^-3 , and 0.8 = 8 * 10^-1 , so you just have to do 24/8 and subtract -3 - (-1) = -2 , so in the end 3 * 10^(-2) = 0.03. If you are already quick with the big number you should get quick with this as well quite easily



Anonymous updated his answer on Sep 06, 2017

Hi Jana,

You can think about this in multiple ways:

1 - Know by heart the main common fractions (i.e. 1/2 all the way to 8/9), this definitely speeds up your habilities.

2 - break big denominators into smaller ones which you know the common fraction for (look point again) (to give an example: lets say you are doing a market sizing and you need to divide 1M ppl by life expectancy of 75 years of age; you may not know 1M/75 but you can break it into (1M/3)*(1/25)=333k*4% which you would be able to do it fairly easy and also explain it in simple terms.

3 - Simplifying a fraction before delving into a division can also speed up the process.


Lets use these tips into the example you provided: 0.024/0.8

So to simplify expression lets simply took one decimal place = 0.24/8 (step 3)

We know that 1/8 its 12.5% (step 1)

in your head 12.5% is dividing by 2, 3 times = 0.24-0.12-0.06-0.03 (final result)


Even though the example you provided was fairly easy this shows that you could simply do the entire process in your head and you could even very quickly walk the interview through these steps if you spoke them out loud.

Hope it helps!


Thai Son replied on Nov 09, 2018

Hi Jana,

I think decimal in general troubles us by the "zero".

In this case you can quickly see that 0.024 = 24/1000 and 0.8 = 8/10. Then 0.024 : 0.8 = 24/1000 x 10/8 = 3/100 = 0.03.

Good luck !

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