Every terminating decimal can be represented as a repeating decimal. For example, 1/2 is a terminating decimal because it equals 0.50000..... but 0.50000... = 0. 4999.... which is a repeating decimal.
To see this, let x = 0.49999... Then 10x = 4.9999.... Subtract x (0.449999... ) to get 9x = 4.50000..... then divide by 9 to get x = 5.00....or simply 5.
The number of digits in the repeating part of a repeating decimal is known as its period. For example, 1/3 = 0.33333... has a period of 1. 1/7 = 0.142857142857.... has a period of 6.
If you multiply a repeating decimal by an integer, the result is always a repeating decimal with the same period. For example, 1/3 * 2 = 0.666666... which also has a period of 1.
If 1/m is a repeating decimal and 1/n is a terminating decimal, then 1/mn is a decimal with a nonperiodic part as long as 1/n and a period the same as 1/n. For example, 1/3 * 1/4 = 1/12 = 0.08333.... The nonperiodic part has length 2 (the 0.08) has length 2 (like 1/4) and the periodic part (the 3333....) has length 1 (like 1/3).
Numbers that are repeating in base 10 may be terminating in some other base, and vice versa. For example, 1/10 is a terminating decimal in base 10 (it is 0.10000...) but a repeating decimal in base 2 (it is 0.001100110011....). And 1/3 is a repeating decimal in base 10, but a terminating decimal in base 3. (It is 0.3333..... in base 10 and 0.10000 in base 3).