Higher January 2023 Paper 2 Q16
16 Use algebra to show that \(\;0.4\dot{3}\dot{8} = \dfrac{217}{495}\)
(2)
| Scheme | Marks |
|---|---|
| eg \(1000x = 438.38\ldots\) \(\phantom{eg 10}\underline{10x = \phantom{43}4.38\ldots}\) or \(100x = 43.838\ldots\) \(\phantom{or 10}\underline{x = \phantom{4}0.438\ldots}\) oe | M1 |
eg \(1000x - 10x = 438.38\ldots - 4.38\ldots = 434\) and \(\dfrac{434}{990} = \dfrac{217}{495}\) or eg \(100x - x = 43.838\ldots - 0.438\ldots = 43.4\) and \(\dfrac{43.4}{99} = \dfrac{217}{495}\) or eg \(1000x - 10x = 38.38\ldots - 0.3838 = 38\) and \(0.4 + \dfrac{38}{990} = \dfrac{4 \times 99 + 38}{990} = \dfrac{434}{990} = \dfrac{217}{495}\) oe working required Answer: Clearly shown | A1 |
| (2) | |
| (2 marks) |
Notes
M1: For selecting 2 correct recurring decimals that when subtracted give a whole number or terminating decimal (43.4 or 434 etc)
eg \(1000x = 438.38\ldots\) and \(10x = 4.38\ldots\)
or \(100x = 43.838\ldots\) and \(x = 0.438\ldots\)
with intention to subtract.
(if recurring dots not shown then showing at least one of the numbers to at least 5sf)
or
\(0.4 + 0.0\dot{3}\dot{8}\) and eg \(1000x = 38.38\ldots\) & \(10x = 0.3838\ldots\), with intention to subtract.
A1: For completion to \(\dfrac{217}{495}\) dep on M1 and use of some algebra