Higher November 2024 Paper 6 Q15
15 Prove that \(1.8\dot{6}\) converts to the fraction \(\dfrac{28}{15}\).
You must show your working. [3]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(1.8\dot{6}\) × by a power of 10 | M1 | e.g. \(10x = 18.6\ldots\) or \(100x = 186.6\ldots\) | Mark similarly the use of other powers of 10 and the use of \(x\) in subtractions |
| Both sides of the subtraction completed to remove recurring digits | M1 | \(90x = 168\) | |
| \(x\) correct as an unsimplified fraction after correct subtraction and stated as equal to \(\frac{28}{15}\) | A1 | \(x = \frac{168}{90} = \frac{28}{15}\) Alternative method: M1 for \(1.8\dot{6} = 1 + 0.66\ldots + 0.2\) M1 for \(= 1 + \frac{2}{3} + \frac{1}{5}\) A1 for \(= 1 + \frac{10 + 3}{15} = \frac{28}{15}\) | |