Higher June 2019 Paper 1 Q15
15 Use algebra to show that the recurring decimal \(0.2\dot{5}\dot{4} = \dfrac{14}{55}\)
(2)
| Scheme | Marks |
|---|---|
| \(x = 0.25454\ldots\) \(100x = 25.454\ldots\) \(10x = 2.5454\ldots\) \(1000x = 254.54\ldots\) | M1 |
Working required eg \(100x - x = 25.454\ldots - 0.254\ldots = 25.2\) and \(\dfrac{25.2}{99} = \dfrac{14}{55}\) or \(1000x - 10x = 254.545\ldots - 2.545\ldots = 252\) and \(\dfrac{252}{990} = \dfrac{14}{55}\) or \(100x - x = 5.4545\ldots - 0.05454\ldots = 5.4\) and \(\dfrac{5.4}{99} = \dfrac{54}{990}\left(= \dfrac{3}{55}\right)\) and \(\dfrac{2 \times 99 + 54}{990} = \dfrac{252}{990} = \dfrac{14}{55}\) or \(\dfrac{5.4}{99} = \dfrac{54}{990} = \dfrac{3}{55}\) and \(\dfrac{11 + 3}{55} = \dfrac{14}{55}\) Answer: show | A1 |
| (2) | |
| (2 marks) |
Notes
M1: For 2 recurring decimals that when subtracted give a whole number or terminating decimal eg 25.2 or 252 etc eg \(100x = 25.454\ldots\) and \(x = 0.25454\ldots\) or \(1000x = 254.54\ldots\) and \(10x = 2.5454\ldots\) with intention to subtract.
(if recurring dots not shown then showing at least the digits 25454, ie 5sf)
or
\(0.2 + 0.0\dot{5}\dot{4}\) and
eg \(x = 0.05454\ldots, 100x = 5.4545\ldots\)
with intention to subtract.
A1: for completion to \(\dfrac{14}{55}\)