4MA0 Higher January 2018 Paper 3 Q16
16 Use algebra to show that the recurring decimal \(0.3\dot{4}\dot{5} = \dfrac{19}{55}\)
(2)
| Scheme | Marks |
|---|---|
| eg \(100x = 34.5\dot{4}\dot{5}\) and \(x = 0.3\dot{4}\dot{5}\) \(100x - x = 34.5\dot{4}\dot{5} - 0.3\dot{4}\dot{5}\) | M1 |
| Shown by an algebraic method | A1 |
| (2) |
Notes
M1: for two decimals that, when subtracted will leave a non-recurring value, and intention to subtract (must show recurring dots or at least 2 of 54 or 45)
A1: must see a correct fraction prior to \(\dfrac{19}{55}\) or division must be clearly shown
Alternative scheme
| Scheme | Marks |
|---|---|
| eg \(10x = 0.\dot{4}\dot{5}\) \(1000x = 45.\dot{4}\dot{5}\) \(1000x - 10x = 45.\dot{4}\dot{5} - 0.\dot{4}\dot{5}\) | M1 |
\(990x = 45\) \(x = \dfrac{45}{990}\) \(0.3\dot{4}\dot{5} = \dfrac{3}{10} + \dfrac{45}{990}\) Answer: Shown by an algebraic method | A1 |
Notes
M1: for two decimals that, when subtracted will leave a non-recurring value, and intention to subtract
A1: for a complete method
(In this alternative, as printed, \(x\) stands for \(0.0\dot{4}\dot{5}\), the part after 0.3)