1.11111111 as a Fraction

Answer

The answer for 1.11111111 as a fraction will be 10/9.

Explanation

Converting a decimal to a fraction is a task for students that can be done easily. You can follow the steps mentioned below to find the answer.

Step 1: Firstly, separate the whole number from the repeating decimal part. The whole number here is 1, and the repeating decimal is 0.11111111. This can be represented as 1 + 0.11111111.

Step 2: To convert 0.11111111 to a fraction, note that it is a repeating decimal. Let x = 0.11111111...

Step 3: Multiply both sides of the equation by 10 to shift the decimal point: 10x = 1.11111111...

Step 4: Subtract the original x equation from this new equation: 10x - x = 1.11111111... - 0.11111111...

Step 5: This results in: 9x = 1

Step 6: Solving for x gives x = 1/9

Step 7: Therefore, 1 + 0.11111111... = 1 + 1/9 = 10/9

Thus, 1.11111111 can be written as a fraction 10/9.

• 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.