Fraction to Decimal Converter

Terminating vs Repeating Decimals

A fraction is a quotient of two integers. When a fraction is converted into a decimal value, it will always either terminate (end) or repeat infinitely in a periodic pattern:

• Terminating Decimal: The division ends with a remainder of 0. This happens if and only if the simplified denominator has no prime factors other than 2 and 5 (e.g. \(3/8 = 0.375\)).
• Repeating Decimal (Recurring): The division continues infinitely with a repeating sequence of digits. It is mathematically denoted by drawing a bar (vinculum) over the repeating period (e.g. \(1/3 = 0.\overline{3}\) or \(1/7 = 0.\overline{142857}\)).