Higher June 2022 Paper 2R Q17
17 Use algebra to show that \(0.3\dot{4}\dot{5} = \dfrac{19}{55}\)
(2)
| Scheme | Marks |
|---|---|
| eg \(x = 0.34545\ldots\) and \(100x = 34.545\ldots\) with intention to subtract OR \(10x = 3.4545\ldots\) and \(1000x = 345.45\ldots\) with intention to subtract Must include algebra as the question asked for ‘using algebra’ | M1 |
eg \(100x - x = 34.545\ldots - 0.34545\ldots\) and \(99x = 34.2\) and \(\dfrac{34.2}{99} = \dfrac{19}{55}\) oe OR \(1000x - 10x = 345.45\ldots - 3.4545\ldots\) and \(990x = 342\) and \(\dfrac{342}{990} = \dfrac{19}{55}\) oe OR \(0.3 + \ldots\) and \((1000x - 10x = 990x = 45)\) and \(0.3 + \dfrac{45}{990} = \dfrac{3 \times 99 + 45}{990} = \dfrac{19}{55}\) oe Answer: shown | A1 |
| (2) | |
| (2 marks) |
Notes
M1: for 2 recurring decimals (they must identify or show the pair they are using) that when subtracted give a whole number or terminating decimal eg \(100x = 34.545\ldots\) and \(x = 0.34545\ldots\) OR \(1000x = 345.45\ldots\) and \(10x = 3.4545\ldots\) with intention to subtract. (If recurring dots not shown then showing at least the digits 34545, i.e. 5sf for one of the numbers that they are using)
OR
\(0.3 + 0.0454545\ldots\) and
Eg \(10x = 0.454545\ldots\) and \(1000x = 45.4545\ldots\)
A1: for completion to \(\dfrac{19}{55}\)