Converting Decimal -0.366666666666 to Fraction

To convert the decimal -0.366666666666 into a fraction, we will follow these steps:

1. Identify the Decimal: The given number is -0.366666666666.
2. Separate the Whole Number: In this case, the whole number part is 0, so we only need to deal with the decimal part: -0.366666666666.
3. Convert to Fraction: The decimal 0.366666666666 can be expressed as:

0.366666666666 is equivalent to 0.37 (for rounding) but we need to recognize that it is a repeating decimal - specifically, we can express this decimal as:

-0.366ar{6}

Where the bar indicates that the '6' repeats indefinitely. To convert this repeating decimal into a fraction:

1. Name the repeating decimal: Let x = -0.366ar{6}
2. Multiply by a power of 10 to shift the decimal point:
   10x = -3.666ar{6}
3. Set up an equation:
   10x = -3.666ar{6}
   x = -0.366ar{6}
4. Now subtract the second equation from the first:
   10x - x = -3.666ar{6} - (-0.366ar{6})
5. Simplifying gives:
   9x = -3.3
6. Now, solve for x:
   x = -3.3 / 9
7. Convert -3.3 to a fraction:
   -3.3 = -33/10, so
   x = -33/10 / 9 = -33/90

After simplifying the fraction:

-33/90 = -11/30 (dividing the numerator and denominator by 3).

Therefore, the final answer is:

-0.366666666666 as a fraction is -11/30.

In summary: -0.366666666666 = -11/30