Express 0.17̅ as a fraction - Edexcel - GCSE Maths - Question 13 - 2022 - Paper 1

To express the repeating decimal 0.17̅ as a fraction, we can follow these steps:

1. Let x equal the repeating decimal:
   Let ( x = 0.171717... )

2. Multiply by 100 to shift the decimal:
   This gives us ( 100x = 17.171717... )

3. Set up an equation to eliminate the decimal:
   Now, we have the two equations: [ x = 0.171717... ] [ 100x = 17.171717... ]

4. Subtract the first equation from the second:
   [ 100x - x = 17.171717... - 0.171717... ] [ 99x = 17 ]

5. Solve for x:
   [ x = \frac{17}{99} ]

Thus, we have expressed the repeating decimal 0.17̅ as the fraction ( \frac{17}{99} ).