14.2857142857 as a Fraction

Answer:

The answer for 14.2857142857 as a fraction will be 100/7.

Explanation:

Converting a decimal to a fraction is a task for students that can be done easily. You can follow the steps mentioned below to find the answer.

Step 1: Firstly, separate the whole number from the repeating decimal part. Here, we have 14 and 0.2857142857... (which is a repeating decimal) becomes 14 + 0.2857142857...

Step 2: To convert the repeating decimal 0.2857142857... into a fraction, recognize the repeating sequence as 285714. This sequence has 6 digits. Therefore, to remove the decimal, multiply the repeating part by 10^6 (or 1,000,000). Let x = 0.2857142857... Then, 1,000,000x = 285714.285714...

Step 3: Subtract the equation x = 0.2857142857... from the equation 1,000,000x = 285714.285714... 1,000,000x - x = 285714.285714... - 0.2857142857... 999,999x = 285714 x = 285714/999999

Step 4: Simplify the fraction 285714/999999 by finding the GCD. In this case, the GCD is 142857. 285714 ÷ 142857 / 999999 ÷ 142857 = 2/7

Step 5: Add the whole number part back to the fractional part. 14 + 2/7 = (14 × 7 + 2) / 7 = 100/7 Thus, 14.2857142857 can be written as a fraction 100/7.

• 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.