0.857142857 as a Fraction

Answer

The answer for 0.857142857 as a fraction will be 6/7.

Explanation

Converting a repeating 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: Let x = 0.857142857... Notice that the decimal part 857142 repeats indefinitely.

Step 2: To eliminate the repeating part, multiply x by 1000000 (since there are 6 repeating digits), giving: 1000000x = 857142.857142857...

Step 3: Subtract the original equation (x = 0.857142857...) from this new equation: 1000000x - x = 857142.857142857... - 0.857142857... 999999x = 857142

Step 4: Solve for x by dividing both sides by 999999: x = 857142/999999 Step 5: Simplify the fraction by dividing the numerator and the denominator by their greatest common divisor, which is 142857: 857142/999999 = 6/7

Thus, 0.857142857 can be written as a fraction 6/7.

• 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.
   
• 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.
   
• Repeating Decimal: A decimal in which one or more digits repeat infinitely.