Table Of Contents
Last updated on March 24th, 2025
Numbers can be categorized into different types. Fraction is one of its kind. It is always represented in the form of p/q, where p is the numerator and q is the denominator. Fraction represents a whole and a fractional part. Decimals represent the fractional part of numbers. For example, 1/2, the numbers in decimal are expressed with a decimal point (.), For example, 0.285714285714, we are going to learn how to convert a decimal to a fraction.
The answer for 0.285714285714 as a fraction will be 2/7.
Converting a repeating decimal to a fraction involves recognizing the repeating part and using algebra. You can follow the steps mentioned below to find the answer.
Step 1: Let x = 0.285714285714...
Step 2: Since the repeating part is 285714 (6 digits), multiply x by 10^6 to shift the decimal point past the repeating part: 1000000x = 285714.285714...
Step 3: Subtract the original equation from this equation to eliminate the repeating decimal: 1000000x - x = 285714.285714... - 0.285714285714... 999999x = 285714
Step 4: Solve for x by dividing both sides by 999999: x = 285714/999999 Step 5: Simplify the fraction by finding the greatest common divisor (GCD) of 285714 and 999999, which is 142857: x = (285714 ÷ 142857) / (999999 ÷ 142857) = 2/7
Thus, 0.285714285714 can be written as a fraction 2/7.