Converting the Decimal -3.11111111111111 to a Fraction

To convert the decimal -3.11111111111111 into a fraction, we follow these steps:

1. Identify the Whole Number: The given decimal is -3.11111111111111. The whole number part is -3.
2. Isolate the Decimal Part: The decimal part is 0.11111111111111. This can also be represented as a repeating decimal, which we can write as 0.1 with a bar over the 1 indicating it repeats: 0.1̅.
3. Convert the Decimal Part into a Fraction: We can convert the repeating decimal 0.1̅ into a fraction using the following method:
1. Let x = 0.1̅: x = 0.1111111111...
2. Multiply x by 10: 10x = 1.1111111111...
3. Subtract the first equation from the second: 10x - x = 1.1111111111... - 0.1111111111...
4. This simplifies to:
9x = 1
5. Solving for x gives: x = 1/9
4. Combine the Whole Number and Fraction: Now we can combine our whole number -3 and the fraction 1/9:

To combine -3 and 1/9, we can express -3 as a fraction:

-3 = -27/9 so we have:
-3 + 1/9 = -27/9 + 1/9 = -26/9.
5. Final Result: Therefore, -3.11111111111111 can be written as a fraction:
-3.11111111111111 = -26/9.

In conclusion, -3.11111111111111 as a fraction is -26/9.