Higher November 2024 Paper 3 Q14
14 Prove algebraically that \(0.4\dot{6}\dot{2}\) can be written as \(\dfrac{229}{495}\) (3)
| Answer | Mark | Mark scheme |
|---|---|---|
| Shown | M1 | for start to find multiples of \(x\) with the same recurring pattern eg for \((10x =)\ 4.626262\ldots\) or \((100x =)\ 46.262626\ldots\) or \((1000x =)\ 462.626262\ldots\) |
| M1 | (dep on M1) for a correct subtraction that would lead to a terminating decimal, eg \((1000x - 10x) = 462.6262\ldots - 4.6262\ldots\ (= 458)\) or \((100x - x) = 46.2626\ldots - 0.4626\ldots\ (= 45.8)\) | |
| C1 | for correct working leading to the correct answer |
Additional guidance
Any recurring notation acceptable throughout.
Proofs with terminating decimals (at least 5 figures) score M1M1C0