How to Write a Repeating Decimal As a Fraction

Fractions convert to decimals and percent.
••• Hemera Technologies/AbleStock.com/Getty Images

A repeating decimal is a decimal that has a repeating pattern. A simple example is 0.33333.... where the ... means continue like this. Many fractions, when expressed as decimals, are repeating. For instance, 0.33333.... is 1/3. But sometimes the repeating portion is longer. For instance, 1/7 = 0.142857142857. However, any repeating decimal can be converted into a fraction. Repeating decimals are often represented with a bar, over the repeating portion.

    Identify the repeating portion. For instance, in 0.33333..... the 3 is the repeating portion. In 0.1428571428, it is 142857

    Count the number of digits in the repeating portion. In 0.3333 the number of digits is one. In 0.142857 it is six. Call this "d."

    Multiply the repeating decimal by 10^d, that is, one with "d" zeroes after it. So, multiply 0.3333.... by 10^1 = 10 to get 3.3333...... Or multiply 0.142857142857 by 10^6 = 1,000,000 to get 142857.142857.....

    Note that the result of this multiplication is a whole number plus the original decimal. For instance 3.33333...... = 3 + 0.33333..... Or, in other words, 10x = 3 + x. With 0.142857, you would get 1,000,000x = 142,857 + x.

    Subtract x from each side of the equation. For example, if 10x = 3 + x, then subtract x from each side to get 9x = 3 or 3x = 1 or x = 1/3 In the other example, 1,000,000x = 142,857 + x, so 999,999x = 142,857 or 7x = 1 or x = 1/7

Related Articles

How to Convert an Infinite Decimal to a Fraction
How to Do Math Problems in Your Head at Lightning Speed
How to Calculate 1/6th of Something
How to Convert an Infinite Decimal to a Fraction
Adding & Subtracting Fractions
Definition of Successor and Predecessor in Math
How to Find the Line of Symmetry in a Quadratic Equation
How to Add & Subtract Fractions With Monomials
How to Find a Percent of a Fraction
How to Subtract Monomials & Binomials
How to Round a Number to the Nearest Tenth
How to Convert a Decimal to a Whole Number
How to Find the Y-Intercept of a Circle
How to Calculate Two Thirds of a Number
How to Find Fraction Sequences
How to Find Linear Functions
How to Write the Remainder As a Whole Number
How to Change Mixed Numbers Into Whole Numbers
How to Easily Convert Celsius to Fahrenheit
How to Do Math Problems in Your Head at Lightning Speed

Dont Go!

We Have More Great Sciencing Articles!