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125 LearnersLast updated on March 8th, 2025
1.111111111 as a Fraction
Numbers can be categorized into different types. 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. Fractions represent 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, 1.111111111, we are going to learn how to convert a decimal to a fraction.
What is 1.111111111 as a Fraction?
Answer
The answer for 1.111111111 as a fraction will be 10/9.
Explanation
Converting a repeating decimal to a fraction can be done by following systematic steps. You can follow the steps mentioned below to find the answer.
Step 1: Let x = 1.111111111...
Step 2: Since the decimal repeats every digit, multiply x by 10 to shift the decimal point one place to the right: 10x = 11.111111111...
Step 3: Subtract the original equation from this new equation to eliminate the repeating part: 10x - x = 11.111111111... - 1.111111111...
Step 4: Simplify the equation: 9x = 10
Step 5: Solve for x by dividing both sides by 9: x = 10/9
Thus, 1.111111111 can be written as a fraction 10/9.
Important Glossaries for 1.111111111 as a Fraction
- Fraction: A numerical quantity that is not a whole number, representing a part of a whole.
- Repeating Decimal: A decimal that has one or more repeating digits or sequence of digits after the decimal point.
- 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.
- Infinite Series: A sequence of numbers in which the sum of all terms can be finite or infinite.
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