0.285714285714 as a Fraction

Answer

The answer for 0.285714285714 as a fraction will be 2/7.

Explanation

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.

• Fraction: A numerical quantity that is not a whole number, representing a part of a whole.

• Decimal: A number that uses the base ten and includes a decimal point to separate the whole part from the fractional part.

• Repeating Decimal: A decimal in which a sequence of digits repeats infinitely.

• Numerator: The top part of a fraction, indicating how many parts of the whole are being considered.

• Denominator: The bottom part of a fraction, showing how many parts make up a whole.