2.857142857 as a Fraction

Answer

The answer for 2.857142857 as a fraction will be 20/7.

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, let's recognize that 2.857142857 is a repeating decimal. We can express it as 2 + 0.857142857...

Step 2: Notice that 0.857142857... is a repeating decimal with a cycle of 6 digits (857142). To convert it to a fraction, let's denote x = 0.857142857...

Step 3: Multiply x by 1,000,000 to shift the decimal point by 6 places: 1000000x = 857142.857142...

Step 4: Subtract x from 1000000x to eliminate the repeating part: 1000000x - x = 857142.857142... - 0.857142857... 999999x = 857142

Step 5: Solve for x: x = 857142/999999

Step 6: Simplify the fraction by finding the GCD of 857142 and 999999, which is 142857: x = 857142 ÷ 142857 / 999999 ÷ 142857 = 6/7

Step 7: Therefore, 2.857142857 = 2 + 6/7 = (14 + 6)/7 = 20/7

Thus, 2.857142857 can be written as a fraction 20/7.

• 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 a digit or a group of digits repeats infinitely.