0.090909 as a Fraction

Answer

The answer for 0.090909 as a fraction will be 1/11.

Explanation

Converting a repeating decimal to a fraction involves a few specific steps. You can follow the steps mentioned below to find the answer.

Step 1: Let x equal the repeating decimal: x = 0.090909...

Step 2: Multiply by a power of 10 to move the decimal point so that the repeating part aligns with itself. Since the repeating part has two digits, multiply by 100: 100x = 9.090909...

Step 3: Subtract the original equation from this new equation to eliminate the repeating part: 100x - x = 9.090909... - 0.090909... 99x = 9

Step 4: Divide both sides by 99 to solve for x: x = 9/99

Step 5: Simplify the fraction by finding the greatest common divisor of 9 and 99, which is 9: 9/99 = 1/11

Thus, 0.090909 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.