1.142857 as a Fraction

Answer

The answer for 1.142857 as a fraction is 8/7.

Explanation

Converting a repeating decimal to a fraction can be accomplished with a systematic approach. You can follow the steps below to find the answer.

Step 1: Identify the repeating part of the decimal. Here, 1.142857 has a repeating sequence of '142857'.

Step 2: Let x = 1.142857142857..., which can be expressed as x = 1 + 0.142857142857....

Step 3: Notice the repeating cycle has six digits. Multiply by 10^6 (1,000,000) to shift the repeating part: 1,000,000x = 1,142,857.142857...

Step 4: Subtract the original equation from this result to eliminate the repeating part: 1,000,000x - x = 1,142,857.142857... - 1.142857... 999,999x = 1,142,856

Step 5: Solve for x by dividing both sides by 999,999: x = 1,142,856/999,999

Step 6: Simplify the fraction. The GCD of 1,142,856 and 999,999 is 142,857. By dividing both numerator and denominator by 142,857, we get: x = 8/7

Therefore, 1.142857 can be expressed as the fraction 8/7.

• 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 indefinitely.

• 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.