0.27272727272 as a Fraction

Answer

The answer for 0.27272727272 as a fraction will be 3/11.

Explanation

Converting a repeating decimal to a fraction can be done by following these steps:

Step 1: Let x = 0.27272727272...

Step 2: Since the decimal repeats every 2 digits, multiply x by 100 to shift the repeating part: 100x = 27.27272727272...

Step 3: Subtract the original x from this equation to eliminate the repeating decimal: 100x - x = 27.27272727272... - 0.27272727272... 99x = 27

Step 4: Solve for x by dividing both sides by 99: x = 27/99

Step 5: Simplify the fraction 27/99. The GCD of 27 and 99 is 9, so divide the numerator and the denominator by 9: 27/99 = 3/11

Thus, 0.27272727272 can be written as the fraction 3/11.

• 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 pattern of one or more digits is repeated indefinitely.