Decimal to Fraction Simplifier

How to calculate a simplified fraction?

To calculate a simplified fraction from a decimal, you first count the number of decimal places to determine the denominator (e.g., 10 for one place, 100 for two, 1000 for three). Once you have the initial fraction, you divide both the numerator and the denominator by their greatest common divisor (GCD) to reach the simplest form.

Fraction = (Decimal × 10^n) / 10^n

Using the simplifier: an example

Let's look at an example using the value 0.625 to see how the conversion process works in practice.

Step-by-step calculation:

1. Multiply 0.625 by 1000 (since there are three decimal places) to get the fraction 625/1000.
2. Find the greatest common divisor (GCD) of 625 and 1000, which is determined to be 125.
3. Divide both the numerator and the denominator by 125 to reach the final simplified fraction of 5/8.

Frequently Asked Questions

What are terminating decimals?

Terminating decimals are numbers that have a specific end point or a finite number of digits following the decimal mark, making them straightforward to convert into fractions.

Can this simplify repeating decimals?

Repeating decimals require a different method involving algebraic subtraction to remove the infinite sequence. This specific calculator is designed for terminating decimals.

How do mixed numbers work?

Mixed numbers are formed when a decimal has a whole number part (e.g., 1.25). The whole number remains separate, and only the fractional part (.25) is simplified and then combined back with the integer.