1.20 Recurring decimals
9 exam questions worth 24 marks. Write your answer, open the mark scheme, then give yourself the marks you earned. Your answers are saved on this device.
0 / 24
What is 0.\dot{7} as a fraction?
Choose one answer.
Correct Not quite: the answer is \( \frac{7}{9} \)
Mark scheme
B: \frac{7}{9}
Model answer
\frac{7}{9} (B). x = 0.777..., 10x = 7.777..., so 9x = 7 and x = 7/9.
Write \frac{5}{6} as a recurring decimal. Use dot notation.
Mark scheme
M1: 5 ÷ 6 = 0.8333...; A1: 0.8 with a dot over the 3
Model answer
5 ÷ 6 = 0.8333... = 0.8̇3 (written 0.8 with a dot above the 3).
Prove that 0.\dot{2}\dot{7} = \dfrac{3}{11}.
Mark scheme
M1: x = 0.2727... and 100x = 27.2727...; M1: 99x = 27; A1: x = 27/99 = 3/11
Model answer
Let x = 0.2727... Then 100x = 27.2727... Subtracting gives 99x = 27, so x = 27/99 = 3/11.
Write 0.\dot{4}\dot{5} as a fraction in its simplest form.
Mark scheme
M1: 100x - x; M1: 99x = 45; A1: 5/11
Model answer
x = 0.4545..., 100x = 45.4545..., so 99x = 45 and x = 45/99 = 5/11.
Write 0.1\dot{6} as a fraction in its simplest form.
Mark scheme
M1: 10x = 1.666... and 100x = 16.666...; M1: 90x = 15; A1: 1/6
Model answer
x = 0.1666..., 10x = 1.666..., 100x = 16.666... Subtract: 90x = 15, so x = 15/90 = 1/6.
Write 0.2\dot{3} as a fraction in its simplest form.
Mark scheme
M1: 10x = 2.333... and 100x = 23.333...; M1: 90x = 21; A1: 7/30
Model answer
10x = 2.333... and 100x = 23.333..., so 90x = 21 and x = 21/90 = 7/30.
Without working out the decimals, which of these fractions is a terminating decimal? Give a reason. \frac{7}{16} \frac{5}{12} \frac{2}{7} \frac{4}{15}
Mark scheme
B1: 7/16; B1: 16 = 2⁴ has only the prime factor 2
Model answer
7/16, because the denominator 16 = 2⁴ has only 2 as a prime factor. 12 = 2² × 3, 7 and 15 = 3 × 5 all contain a prime factor that is not 2 or 5.
Write 0.\dot{1}2\dot{3} as a fraction in its simplest form.
Mark scheme
M1: 1000x = 123.123...; M1: 999x = 123; A1: 41/333
Model answer
x = 0.123123..., 1000x = 123.123..., so 999x = 123 and x = 123/999 = 41/333.
Prove that 0.4\dot{5} = \dfrac{41}{90}.
Mark scheme
M1: x = 0.4555..., 10x = 4.555..., 100x = 45.555...; M1: subtracts 100x - 10x; M1: 90x = 41; A1: x = 41/90
Model answer
Let x = 0.45555... Then 10x = 4.5555... and 100x = 45.5555... Subtract: 90x = 41, so x = 41/90.
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