How to avoid repeating decimals?

Answer 1

You can't, really. Repeating decimals appear whenever the denominator of a fraction in simplest terms has any prime factor other than 2 or 5.To avoid them, you can do divisions that don't involve those denominators/divisors.

You can also recognize that "infinite precision" is not required for most practical applications, and round the result to an appropriate number of decimals. What is appropriate will depend on the specific application, but 3-4 significant digits is quite often enough.

Answer 2

A repeating decimal occurs when you divide by a number which has any factor other than 2 or 5. To avoid the repeating decimal, leave it as a fraction of one integer over another.