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Archit Sharma
Archit Sharma

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Why do computers suck at math?

#javascript #webdev #beginners #programming
I discovered something strange when experimenting with JavaScript a few days ago, so I did some research and found my answers.
I'm writing this article in the hopes that some of you will find it useful or mayΒ learn something new.

I used to believe that computers were better at math than humans, until I tried adding 0.1 + 0.2 and got the result 0.30000000000000004 in my browser console.

0.1 + 0.2
Then I performed this comparison 0.1+0.2===0.3 and got the output false.

0.1+0.2===0.3
I initially believed it was a bug in JavaScript, so I attempted the same thing in Java and Python and had the same result in both.

After doing a lot of research, I concluded this is not an bug.
I found out this is math: floating-point arithmetic.
Let's go a little deeper to see what's going on behind the scenes.

Computers have a limited amount of memory and so they need to make a trade-of between range and precision.

Numbers in JavaScript should be stored within 64 bits, which means we can have integers accurate up to 15 digits and a maximum of 17 numbers after the decimal point. It is called a floating point because there is no fixed number of digits before or after the decimal point, allowing it to represent a wide range of numbers both big and small.

The problem is that computer use a Base-2 system i.e. binary while humans use a Base-10 system that leads to rounding errors when all the memory has been used up.

base2 to base10

This is the reason behind getting 0.1 + 0.2 = 0.30000000000000004.

Thank you for reading this article; I have not detailed the entire math behind it, but only enough for you to comprehend what's going on.

Top comments (9)

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ryencode profile image
Ryan Brown •

Back when my org still had Programming Summer Students/Interns, this usually came up every other year.

  1. Student uses float for money values
  2. Total of extended price: sum(qty*price) != Expected Value
  3. Talk about precision with regard to basic types and why many languages have a Decimal type
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iarchitsharma profile image
Archit Sharma •

wow that's cool

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fjones profile image
FJones •

This is actually missing a huge lot of context. Base2 vs Base10 has little to do with floating-point precision (in fact, Base2 has very much the same concept of fractions as Base10, i.e. 0.12 is Β½.)

The problem doesn't come from binary, it stems from the fact that binary needs a lot more positions to represent values than decimal, which makes fractions a particularly nasty scaling issue. Floating-point values are encoded in a very different format, which optimizes for space efficiency at the cost of accuracy, hence the funny edge cases. (Though per the specification of that encoding, there's no real precise values anyway, barring 0)

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pengeszikra profile image
Peter Vivo •

I use this solution for give limit decimal place.

export const epsilonN = N => num => Math.round( num * N + Number.EPSILON ) / N;
export const epsilon = epsilonN(1e7);
export const epsilon2 = epsilonN(1e2);
export const epsilon3 = epsilonN(1e3);
Enter fullscreen mode Exit fullscreen mode 
epsilon(.1 + .2);
// 0.3
Enter fullscreen mode Exit fullscreen mode
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lexlohr profile image
Alex Lohr •

It's actually the opposite: floating point maths sucks at being expressed precisely with limited size binary numbers.

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jonrandy profile image
Jon Randy πŸŽ–οΈ •

Being a sophomore in Computer Science (according to your bio) - I am shocked that you did not know this. What has happened to teaching of CS???

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iarchitsharma profile image
Archit Sharma •

I am student of Computer Science Engineering!!!
The core studies begin in the second year of college; the first year was devoted to common engineering disciplines (Physics, Chemistry, Math etc.)
Everything I've learnt thus far is on my own.
and I didn't know this was so common...πŸ€·β€β™‚οΈ

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jonrandy profile image
Jon Randy πŸŽ–οΈ •

TBH I don't have a degree, but I do know plenty of people who did CS degrees and they all know this. I learned this about age 11 (35 years ago! Seems like forever)

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iarchitsharma profile image
Archit Sharma •

Well, I'm sure none of the folks you know got their CS degree from India.

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