Convert decimal numbers to fractions instantly
The decimal is expressed as a fraction by placing it over a power of 10 based on the number of decimal places (e.g., 0.75 = 75/100). The fraction is then simplified by dividing both numerator and denominator by their Greatest Common Divisor (GCD).
Fractions are essential in cooking (measuring ingredients), engineering (precise measurements), and math homework. Many real-world quantities are more intuitive as fractions -- like 1/3 of a cup rather than 0.333 cups.
The result shows the simplest fraction equivalent of your decimal. A simplified fraction has no common factors between numerator and denominator. For example, 0.375 becomes 3/8 because 375/1000 reduces by dividing both parts by 125.
Repeating decimals have specific fraction equivalents: 0.333... = 1/3, 0.166... = 1/6. For terminating decimals, count the decimal places to determine the denominator. When in doubt, enter the full decimal for the most accurate fraction conversion.
To convert a decimal to a fraction, write the decimal over a power of 10 based on the number of decimal places. For example, 0.75 has two decimal places, so it becomes 75/100. Then simplify by dividing both the numerator and denominator by their greatest common divisor (GCD), giving you 3/4.
To convert a repeating decimal to a fraction, set the decimal equal to a variable x, multiply both sides by a power of 10 to shift the repeating block, then subtract the original equation. For example, if x = 0.333..., then 10x = 3.333..., so 10x - x = 3, giving 9x = 3 and x = 1/3.
To simplify a fraction, find the greatest common divisor (GCD) of the numerator and denominator, then divide both by that number. For example, to simplify 12/18, the GCD of 12 and 18 is 6, so divide both by 6 to get 2/3. A fraction is fully simplified when the numerator and denominator share no common factors other than 1.