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Step 1:I'll solve this step by step, following the LaTeX formatting guidelines precisely:
Step 2:: Convert the fraction \frac{5}{6} to a decimal
- $$5 \div 6 = 0.8333333...
- Divide 5 by 6 using long division
Step 3:: Identify the decimal pattern
- This can be written as $$0.\overline{8}$$ or $$0.8333333...
- The decimal representation has a repeating digit sequence
Step 4:: Determine decimal classification
- Therefore, $$-\frac{5}{6}$$ is a repeating decimal
- A repeating decimal has a digit or sequence of digits that repeat endlessly
Step 5:: Confirm the sign
- $$-\frac{5}{6} = -0.\overline{8}
- The original fraction is negative, so the decimal is also negative
Final Answer
-\frac{5}{6} is a repeating decimal.
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