Higher November 2024 Paper 1 Q12
12
(a) Convert \(\;\dfrac{27}{11}\;\) to a recurring decimal. [2 marks]
(b) Convert \(\;0.1\dot{5}\;\) to a fraction. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Division of 27 by 11 seen with correct evaluation to least 2.4 or division of 5 by 11 seen with correct evaluation to least (0).4 or 2.45… | M1 | eg \(\begin{array}{r} 2.4\phantom{000} \\ 11\,\big)\overline{27.0000} \end{array}\) |
| \(2.\dot{4}\dot{5}\) or \(2.\overline{45}\) | A1 | condone 2.4545.. |
Additional guidance
| If the answer is given as 2.4545… there must be at least four digits after the decimal point and at least two dots | |
| eg 2.454545.. | M1A1 |
| eg 2.4545 | M1A0 |
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1: using \(x = 0.155\ldots\) | ||
| Multiplication by a power of 10 with correct result | M1 | eg \(10x = 1.55\ldots\) or \(100x = 15.55\ldots\) or \(1000x = 155.55\ldots\) any or no letter |
| Correct equation formed from subtraction of two equations to eliminate recurring digits or correct fraction with a decimal numerator | M1dep | eg \(9x = 1.4\) or \(90x = 14\) or \(99x = 15.4\) eg \(\dfrac{15.4}{99}\) |
| \(\dfrac{7}{45}\) | A1 | oe fraction eg \(\dfrac{14}{90}\) or \(\dfrac{154}{990}\) |
| Alternative method 2: using \(x = 0.055\ldots\) | ||
| Correct equation formed from subtraction of two equations to eliminate recurring digits or correct fraction, which may include a decimal numerator | M1 | eg \(9x = 0.5\) or \(90x = 5\) or \(99x = 5.5\) eg \(\dfrac{55}{990}\) or \(\dfrac{5.5}{99}\) |
| \(\dfrac{1}{10}\) + their correct fraction, which may include a decimal numerator | M1dep | eg \(\dfrac{1}{10} + \dfrac{5}{90}\) |
| \(\dfrac{7}{45}\) | A1 | oe fraction eg \(\dfrac{14}{90}\) or \(\dfrac{154}{990}\) |
Additional guidance
Up to M2 may be awarded for correct work with no answer or incorrect answer, even if this is seen amongst multiple attempts
Ignore incorrect simplifying if correct fraction seen
Unless recovered, recurring decimals must be in correct notation or denoted by at least two repeated digits after the decimal point with at least two dots