Decimal to Fraction Calculator

Converting a decimal to a fraction depends on whether the decimal terminates or repeats infinitely. For a terminating decimal like 0.75, you place the digits after the decimal point over a power of 10 determined by the count of decimal places (in this case, 75 over 10^{2} or 100). The fraction is then simplified by dividing both the numerator and denominator by their greatest common divisor (GCD). For repeating decimals, such as 0.333..., algebraic expansion is used: let x = 0.333..., then 10x = 3.333..., and subtracting the two yields 9x = 3, resulting in the fraction 3/9, which simplifies to 1/3.

Let us walk through converting the decimal 0.625 into a fully reduced fraction. First, identify the number of decimal places, which is three. This means we place the entire fractional part over 10 raised to the power of 3, which equals 1,000. We write this as the fraction 625 / 1,000. Next, we find the greatest common divisor (GCD) of 625 and 1,000. Both numbers are divisible by 125. Dividing the numerator by 125 gives us 5, and dividing the denominator by 125 gives us 8. Thus, 0.625 simplifies cleanly into the exact fraction 5/8.

Always check if your decimal has a repeating pattern before conversion, as this requires a completely different algebraic approach than terminating numbers. When reducing large fractions manually, finding the prime factorization of both the numerator and denominator can speed up the simplification process significantly. Lastly, remember that improper fractions (where the numerator is larger than the denominator) should be converted into mixed numbers if the context requires a whole number alongside a proper fraction.