Decimal Fractions

Terminating Decimals and Repeating Decimals

Repeating Decimals (Nonterminating Decimals)

Some common fractions, when we divide them out, never have a remainder of zero, instead the quotient forms a nonzero repeating pattern that never ends. The fraction is the most familiar of these type fractions that repeat in decimal form. If we divide 1 ÷ 3,  we will get 0.333333 . . . and these threes will continue on forever, called a repeating decimal. The common notation we use to write these repeating decimals is to place a bar above the repeating digits, e.g., . The bar over the three means that the three repeats infinitely many times.  

Important Note: Do not say or write . This is a false statement since   but , an approximation not an equality. If the decimal is a repeating decimal, you must use either the ellipsis (…) or the repeat bar.

Most repeating decimals have several digits that repeat. For instance, .

Example: Express three-sevenths in decimal form.

Hence, we have .

Repeating decimal - Wikipedia, the free encyclopedia

Self-Check Problem

Express five-sixths in decimal form.

Solution

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