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.

• 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.