In the most commonly used place value, the decimal system, numbers smaller than 1 can be expressed as fractions, called decimal fractions. In this system, the decimal fractions are expressed in terms of tenths, hundredths, thousandths, and so on. For example, for the fraction ½, or 1 divided by 2, the decimal fraction is 0.5; and vice versa, the decimal fraction 0.5, or 5/10ths, is equal to ½.

Not all fractions are so easily converted to decimals. It depends on the type of number, especially if it is an irrational or rational number. Some decimal fractions include an infinite number of decimal places to be expressed exactly; something that is not possible as far as we know (who can write an infinite number of numbers?). And some decimal fractions repeat forever, such as 1/3 _ 0.3333.…