Can every repeating fraction be represented as a decimal? - Answers

Yes, because a fraction a/b where a and b are integer, and b is different than 0, is a rational number which are whole numbers or decimal numbers, where the decimal part is finite or repeating blocks. Conversely, decimals that do not repeat or terminate cannot be represented as a fraction. For example, in a right isosceles triangle with side a and hypotenuse (square root of 2)a, we can't represent as a fraction [(square root of2)a]/a (hypotenuse/side), because will have an irrational number (square root of 2). Here is one fun thing to know about repeating decimals. If you look at the repeating decimals formed by taking 1/n, where n is a Prime number that is not 2 or 5, you will see that the length of the (smallest choice of) the part that repeats [i.e., 3, not 333, for 0.3333...] is: 1.always less than or equal to n-1, 2. equal to n-1 only for some of these prime numbers. 3. always a divisor of n-1.