How Is a Fraction Converted to a Decimal?

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A fraction can be converted to its equivalent decimal by dividing its numerator by its denominator. For example, the fraction 3/4 can be converted to a decimal by dividing its numerator (3) by its denominator (4), which results in 0.75, its equivalent decimal. The fraction 5/8 can be similarly converted to a decimal by dividing 5 by 8, which results in 0.625.

Some fraction-to-decimal conversions will result in a non-terminating, repeating decimal. For example, when the numerator 2 is divided by the denominator 3 to convert 2/3 to a decimal, the result is 0.666666666... The "..." at the end of the decimal indicates that the numbers to the right of the decimal point will continue endlessly. This decimal conversion result, in which the digit 6 repeats itself, can also be represented either by rounding up to 0.67 or by writing it as 0.6 with a horizontal bar above the 6. In the latter representation, the decimal would be read as "zero point six repeating." Some calculators use the rounding-up approach to display a non-terminating decimal.

If a rational number fraction contains a denominator which only has a prime factor of 2 or 5, or prime factors of both 2 and 5, it can be expressed as a finite decimal, rather than a nonterminating decimal. For example, 1/2 = 0.5, 1/5 = 0.2 and 1/10 = 0.1. For those rational number fractions whose denominators contain prime factors other than 2 or 5, the conversion will result in a non-terminating decimal, such as 1/3 = 0.333333... or 1/9 = 0.111111...