Converting a decimal to a fraction means expressing a decimal number as a ratio of two integers. Every decimal number can be represented as a fraction, which is often more precise and easier to work with in mathematical calculations.
For example, the decimal 0.75 can be written as the fraction 3/4. This conversion is useful in many areas of mathematics, including algebra, calculus, and everyday calculations where fractions are preferred over decimals.
Follow these steps to convert a decimal to a fraction:
For a decimal with n decimal places:
Decimal = (Decimal × 10ⁿ) / 10ⁿ
Then simplify by dividing by GCD
Problem: Convert 0.625 to a fraction
Solution:
Repeating decimals like 0.333... convert to fractions using algebra. For 0.333..., let x = 0.333..., then 10x = 3.333..., and 10x - x = 3, so x = 1/3.
Terminating and repeating decimals can be converted to fractions. Irrational numbers like pi (π) or sqrt(2) have non-repeating, non-terminating decimals that cannot be expressed as exact fractions.
First convert the whole number separately, then add the fractional part. For example, 2.75 = 2 + 0.75 = 2 + 3/4 = 11/4.