Higher November 2017 Paper 1 Q26
26
(a) \(0.\dot{7} = \dfrac{7}{9}\)
Use this fact to show that \(\quad 0.0\dot{7} = \dfrac{7}{90}\) [1 mark]
(b) Using part (a) or otherwise, convert \(\quad 0.2\dot{7} \quad\) to a fraction.
Give your answer in its simplest form. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(0.\dot{7} \div 10 = 0.0\dot{7}\) and \(\dfrac{7}{9} \div 10 = \dfrac{7}{90}\) or \(0.0\dot{7} \times 10 = 0.\dot{7}\) and \(\dfrac{7}{90} \times 10 = \dfrac{7}{9}\) or \(0.\dot{7} \div 10 = 0.0\dot{7}\) and \(\dfrac{7}{90} \times 10 = \dfrac{7}{9}\) or because the decimal is divided by 10 the 9 has to be multiplied by 10 | B1 | oe |
Additional guidance
| Algebraic methods | B0 |
| Division of 7 by 90 | B0 |
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(0.2 + 0.0\dot{7}\) or \(\dfrac{2}{10} + \dfrac{7}{90}\) | M1 | |
| \(\dfrac{18}{90} + \dfrac{7}{90}\) or \(\dfrac{25}{90}\) | M1dep | |
| \(\dfrac{5}{18}\) | A1 | |
| Alternative method 2 | ||
| \(10x = 2.777\)… or \(100x = 27.777\)… | M1 | Any letter |
| \(10x - x = 2.777\)… \(-\) 0.277… or \(9x = 2.5\) or \(\dfrac{2.5}{9}\) or \(100x - x = 27.777\)… \(-\) 0.277… or \(99x = 27.5\) or \(\dfrac{27.5}{99}\) or \(100x - 10x = 27.777\)… \(-\) 2.777… or \(90x = 25\) or \(\dfrac{25}{90}\) | M1dep | oe |
| \(\dfrac{5}{18}\) | A1 | |