posted 12 years ago
Yes, 1/3 in base 10 is a good example.
In representing 1/3 as a base-10 decimal, we might start with 0.3, which is 3/10. This is an approximation of 1/3. If we wanted to be more precise, we could add another digit, making it 0.33, which is 33/100. This is a better approximation (more precise), but still not exact. So we continue adding digits, getting closer and closer to 1/3 (adding precision), but never quite reaching it an exact representation.
Now suppose we had a limit on the number of digits we can use. Say, for example, we could not use any more than 4 digits to the right of the decimal. So when we try to represent 1/3, the best precision we can get is 3333/10000, which is not equal to 1/3. On the other hand, we have no problem representing 1/4 exactly as 0.25 because it fits within that limit.
Potential loss of precision in a computer is similar, using a base 2 system subject to the bit limits of floats or doubles.
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