Fraction to Decimal Converter

A fraction and a decimal are two ways to describe the same number. The fraction a/b means a divided by b, so converting it to decimal form is fundamentally a division problem. This converter carries out that division digit by digit, identifies whether the decimal ends or repeats, and marks a recurring block with parentheses. For example, 1/8 becomes 0.125, while 2/3 becomes 0.(6), meaning the digit 6 continues forever. A decimal terminates when the reduced denominator contains no prime factors other than 2 and 5. This follows from our base-ten number system because ten is 2 × 5. The fraction 3/40 terminates because 40 equals 2 cubed times 5, while 1/6 repeats because the reduced denominator still contains a factor of 3. Reducing first matters: 3/6 has denominator 6 as written, but it simplifies to 1/2 and therefore terminates at 0.5. Long division explains where repeating decimals come from. At each step, the remainder is multiplied by ten and divided by the denominator to obtain the next digit. There are only finitely many possible nonzero remainders. If a remainder reaches zero, the expansion terminates. If a remainder appears for a second time, all subsequent division steps repeat in the same order, creating a recurring cycle. The converter remembers each remainder so it can identify the exact start and length of that cycle rather than merely rounding a floating-point value. Improper fractions are supported as well. Dividing 7 by 4 gives a whole-number part of 1 and a remainder of 3, so the decimal is 1.75. Negative signs are normalized and placed before the complete decimal. A denominator of zero is rejected because division by zero is undefined. For ordinary classroom fractions, the displayed cycle gives an exact representation, while unusually long cycles are limited to keep the result readable. Decimal form is convenient for money, measurements, percentages, spreadsheets, and comparisons. Exact fractions are often preferable in algebra and symbolic work, especially when a decimal repeats forever. This tool shows both the decimal classification and the reduced fraction so you can choose the form best suited to the task. Use it to check long division, recognize recurring patterns, or quickly translate fractional data into decimal notation.