1.19 Converting between fractions, decimals and percentages
9 exam questions worth 19 marks. Write your answer, open the mark scheme, then give yourself the marks you earned. Your answers are saved on this device.
0 / 19
What is 0.07 written as a percentage?
Choose one answer.
Correct Not quite: the answer is 7%
Mark scheme
B: 7%
Model answer
7% (B). Multiply by 100: 0.07 × 100 = 7%.
Write 35% as a fraction in its simplest form.
Mark scheme
M1: 35/100; A1: 7/20
Model answer
35% = 35/100 = 7/20.
Write \frac{3}{8} (a) as a decimal (b) as a percentage.
Mark scheme
B1: 0.375; B1: 37.5%
Model answer
(a) 3 ÷ 8 = 0.375. (b) 0.375 × 100 = 37.5%.
Write (a) 0.6 (b) 2.4 as fractions in their simplest form.
Mark scheme
B1: 3/5; B1: 2 2/5 or 12/5
Model answer
(a) 0.6 = 6/10 = 3/5. (b) 2.4 = 2 4/10 = 2 2/5 = 12/5.
Write \dfrac{7}{20} as a percentage.
Mark scheme
M1: 7 ÷ 20 = 0.35 or 35/100; A1: 35%
Model answer
7/20 = 35/100 = 35%.
Write these in order of size, smallest first. 0.45 \frac{2}{5} 42\% \frac{9}{25}
Mark scheme
M1: converts to the same form; A1: 0.45, 0.4, 0.42, 0.36; A1: 9/25, 2/5, 42%, 0.45
Model answer
As decimals: 0.45, 0.4, 0.42, 0.36. Smallest first: 9/25, 2/5, 42%, 0.45.
Which of these fractions gives a recurring decimal?
Choose one answer.
Correct Not quite: the answer is \( \frac{5}{12} \)
Mark scheme
C: \frac{5}{12}
Model answer
\frac{5}{12} (C). 12 = 2² × 3 has a prime factor 3, so 5/12 recurs; the others have only 2 and 5 in the denominator.
Ali scored \frac{27}{40} in a test. Ben scored 66% in the same test. Who did better? You must show your working.
Mark scheme
M1: converts one to the other form; A1: 67.5% (or 0.675 / 0.66); A1: Ali
Model answer
27/40 = 0.675 = 67.5%, which is greater than 66%. Ali did better.
Explain why \frac{3}{8} is a terminating decimal but \frac{5}{12} is not. Work out each as a decimal.
Mark scheme
B1: 3/8 = 0.375; B1: 5/12 = 0.41666... (recurring); B1: 8 = 2³ has only the prime factor 2 whereas 12 = 2² × 3 has a factor 3
Model answer
3/8 = 0.375 which ends. 5/12 = 0.41666... which recurs. 8 = 2 × 2 × 2 so only 2 is a prime factor; 12 = 2 × 2 × 3 includes 3, so the decimal never ends.
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