To convert the decimal -3.11111111111111 into a fraction, we follow these steps:
- Identify the Whole Number: The given decimal is -3.11111111111111. The whole number part is -3.
- 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: 0.1Ì….
- Convert the Decimal Part into a Fraction: We can convert the repeating decimal 0.1Ì… into a fraction using the following method:
- Let x = 0.1Ì…:
x = 0.1111111111... - Multiply x by 10:
10x = 1.1111111111... - Subtract the first equation from the second:
10x - x = 1.1111111111... - 0.1111111111... - This simplifies to:
- Solving for x gives:
x = 1/9 - Combine the Whole Number and Fraction: Now we can combine our whole number -3 and the fraction 1/9:
- Final Result: Therefore, -3.11111111111111 can be written as a fraction:
9x = 1 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. -3.11111111111111 = -26/9. In conclusion, -3.11111111111111 as a fraction is -26/9.