0.142857142857 as a Fraction

Answer

The answer for 0.142857142857 as a fraction will be 1/7.

Explanation

Converting a repeating decimal to a fraction is a task that can be done easily by following a systematic approach. You can follow the steps mentioned below to find the answer.

Step 1: Identify the repeating part of the decimal. Here, 0.142857142857... has a repeating block of 142857.

Step 2: Let x = 0.142857142857...

Step 3: Multiply x by 1000000 (since the repeating block is 6 digits long) to shift the decimal point: 1000000x = 142857.142857...

Step 4: Subtract the original x from this equation to eliminate the repeating part: 1000000x - x = 142857.142857... - 0.142857142857...

Step 5: Simplify the equation: 999999x = 142857

Step 6: Solve for x by dividing both sides by 999999: x = 142857/999999

Step 7: Reduce the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 142857: 142857/999999 = 1/7

Thus, 0.142857142857 can be written as a fraction 1/7.

• 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 fraction in which a figure or group of figures is repeated 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.