Higher November 2021 Paper 1 Q18
18 \(0.4\dot{x}\) is a recurring decimal.
\(x\) is a whole number such that \(1 \leqslant x \leqslant 9\)
Find, in terms of \(x\), the recurring decimal \(0.4\dot{x}\) as a fraction.
Give your fraction in its simplest form.
Show clear algebraic working.
(3)
| Scheme | Marks |
|---|---|
| E.g. \(y = 0.4x\ldots\) and \(10y = 4.x\ldots\) \((10y - y = 4.x - 0.4\) oe\()\) or \(10y = 4.x\ldots\) and \(100y = 4x.x\ldots\) \((100y - 10y = 4x - 4\) oe\()\) or \(100y = 4x.x\ldots\) and \(1000y = 4xx.x\ldots\) \((1000y - 100y = 4xx - 4x\) oe\()\) | M1 |
E.g. \(9y = 4\dfrac{x}{10} - \dfrac{4}{10} = \dfrac{40 + x - 4}{10}\) oe or \(90y = 40 + x - 4\) oe or \(900y = 400 + 10x + x - 40 - x\) oe | M1 |
Working required Answer: \(\dfrac{36 + x}{90}\) | A1 |
| (3) | |
| (3 marks) |
Notes
M1: for selecting 2 correct recurring decimal expressions and then a demonstration to subtract
(If recurring dots not shown then allow each expression to 1 dp
e.g. \(y = 0.4x\ldots\) and \(100y = 4x.x\ldots\) as a pair and \(100y - y\) or \(4x.x\ldots - 0.4x\ldots\))
or an answer of \(y = \dfrac{4x - 4}{90}\) oe
M1: for a correct subtraction with correct expressions simplified
A1: dep on M2 oe