https://file.aiquickdraw.com/mathbot/file/1727272111102h07uh83w.jpg

To convert \( 1.27\overline{7} \) (a repeating decimal) into a fraction, follow these steps:

1. Let \( x = 1.27\overline{7} \). 
2. To remove the repeating decimal, multiply by 10 to shift one decimal place to the right:
   \[
   10x = 12.77\overline{7}
   \]
3. Subtract the original equation from this new equation:
   \[
   10x - x = (12.77\overline{7} - 1.27\overline{7})
   \]
   Simplifying this gives:
   \[
   9x = 11.5
   \]
4. Solve for \( x \) by dividing both sides by 9:
   \[
   x = \frac{11.5}{9} = \frac{115}{90}
   \]
5. Simplify the fraction \( \frac{115}{90} \) by dividing both the numerator and denominator by 5:
   \[
   \frac{115}{90} = \frac{23}{18}
   \]
6. Since the original number was a mixed decimal, we add the 1 from \( 1.27\overline{7} \) back to get the final answer:
   \[
   1\frac{5}{18}
   \]

Therefore, \( 1.27\overline{7} \) as a fraction is \( 1\frac{5}{18} \), which matches one of the options.

Would you like further explanation on any steps?

### Here are 5 related questions for more practice:
1. How do you convert

How do you write 1.27 (with 7 repeating) as a fraction?

Learn how to convert the repeating decimal 1.27̅ into a fraction. This detailed guide explains each step, including algebraic manipulation and fraction simplification. Ideal for students in Grades 6-8.

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