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So, this is a great explanation. I have never heard it expressed this way and I love it. However, I am a little confused. In your first paragraph you say that
by Nemi 11y ago
So, this is a great explanation. I have never heard it expressed this way and I love it.
However, I am a little confused. In your first paragraph you say that 10's prime factors are 5 and 2, so 1/10 can be expressed cleanly. In paragraph two you say that binary only has a prime factor of 2, but 10 is divisible by 2, so why doesn't 1/10 express cleanly in binary?
- aeorgnoieang 11y agoA fraction can only be expressed 'cleanly' if its denominator uses only the prime factors of the base.
- btilly 11y agoFor example, 30 is divisible by 10, but 1/30 is not represented cleanly in base 10.
- such_a_casual 11y agoIn the fraction 1/10, the denominator is 10. The prime factors of 10 are 2 and 5. Binary does not contain the prime factor of 5 necessary to represent 1/10 cleanly as a decimal. It only contains the 2. Similarly, the prime factors for 1/6 would be 3 and 2. In a base 10 number system, you only have the 2. So you end up with a repeating decimal (0.1666666).