# Why computers can’t represent 0.3 accurately

Contents

**Most people know that adding up 0.1 + 0.2 equals 0.3. However computers represent it as 0.30000000000000004 .**

Here is a screenshot of it in python3

Your first thought might be that this is just some kind of error. Well its not

# Why does this happen?

Fractions can be represented precisely in the base 10 system (used by humans) if a prime factor of the base is used (10).

- 2 and 5 are the prime factors of 10.
- 1/2, 1/4, 1/5 (0.2), 1/8, and 1/10 (0.1) can be expressed precisely as a result of denominators use prime factors of 10.
- Whereas, 1/3, 1/6, and 1/7 are repeating decimals as a result of denominators use a prime factor of 3 or 7. On the other hand, fractions can be represented precisely in the base 2 (binary) system (used by computers) if a prime factor of the base is used.
- 2 is the only prime factor of 2.
- So 1/2, 1/4, 1/8 can all be expressed precisely because the denominators use prime factors of 2.
- Whereas 1/5 (0.2) or 1/10 (0.1) are repeating decimals. When you perform math on these repeating decimals, you end up with leftovers which carry over when you convert the computer’s base-2 (binary) number into a more human-readable base-10 representation.

Read more

0.300.com:

https://0.30000000000000004.com/

Wikipedia:

https://en.wikipedia.org/wiki/Floating-point_arithmetic

https://0.30000000000000004.com/

Wikipedia:

https://en.wikipedia.org/wiki/Floating-point_arithmetic

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