0.0909090909 as a Fraction

Answer

The answer for 0.0909090909 as a fraction will be 1/11.

Explanation

Converting a repeating decimal to a fraction can be a bit more complex than a terminating decimal, but it can be done by following the steps below.

Step 1: Let x equal the repeating decimal: x = 0.0909090909...

Step 2: Multiply x by a power of 10 to shift the decimal point to the right until the repeating part aligns: 100x = 9.0909090909...

Step 3: Subtract the original equation (Step 1) from this equation: 100x - x = 9.0909090909... - 0.0909090909... 99x = 9

Step 4: Solve for x by dividing both sides by 99: x = 9/99 Step 5: Simplify the fraction by finding the greatest common divisor (GCD) of 9 and 99, which is 9: 9/99 = 1/11

Thus, 0.0909090909 can be written as a fraction 1/11.

• 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.

• Repeating Decimal: A decimal in which a digit or group of digits repeats infinitely.

• 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.