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116 LearnersLast updated on March 24th, 2025
0.0909090909 as a Fraction
Numbers can be categorized into different types. A fraction is one of its kinds. It is always represented in the form of p/q, where p is the numerator and q is the denominator. A fraction represents a whole and a fractional part. Decimals represent the fractional part of numbers. For example, 1/2, the numbers in decimal are expressed with a decimal point (.), For example, 0.0909090909, we are going to learn how to convert a decimal to a fraction.
What is 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.
Important Glossaries for 0.0909090909 as a Fraction
- 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.
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