1MA0 Higher June 2015 Paper 1 Q21
21 \(x = 0.0\dot{4}\dot{5}\)
Prove algebraically that \(x\) can be written as \(\dfrac{1}{22}\) (3)
| Answer | Mark | Notes |
|---|---|---|
| Proof | 3 | M1 for \((x =)\) 0.04545(...) or \(1000x = 45.4545(...)\), accept \(1000x = 45.\dot{4}\dot{5}\) or \(100x = 4.54545(...)\), accept \(100x = 4.\dot{5}\dot{4}\) or \(10x = 0.4545(...)\), accept \(10x = 0.\dot{4}\dot{5}\) M1 for finding the difference between two correct, relevant recurring decimals for which the answer is a terminating decimal A1 (dep on M2) for completing the proof by subtracting and cancelling to give a correct fraction eg \(\dfrac{45}{990} = \dfrac{1}{22}\) or \(\dfrac{4.5}{99} = \dfrac{1}{22}\) |