Each number below contains the digit 6. Write down the value of the digit 6 in each number.
(a)3.6(1)
(b)5.26(1)
(c)7.406(1)
(Total for Question 1 is 3 marks)
2
Write these numbers in order of size, starting with the smallest: 0.5, 0.45, 0.505, 0.454
(Total for Question 2 is 2 marks)
3
Which of these decimals is the largest?
A) 0.59
B) 0.6
C) 0.099
D) 0.508
(Total for Question 3 is 1 mark)
4
The number 5.867 is to be rounded.
(a)Round 5.867 to 1 decimal place.(1)
(b)Round 5.867 to the nearest whole number.(1)
(Total for Question 4 is 2 marks)
5
Calculate the answer to each of the following.
(a)3.45 + 2.8(2)
(b)7.6 - 2.85(2)
(c)5.09 + 1.351(2)
(Total for Question 5 is 6 marks)
6
Work out 0.482 multiplied by each of the following.
(a)0.482 x 10(1)
(b)0.482 x 100(1)
(c)0.482 x 1000(1)
(Total for Question 6 is 3 marks)
7
Work out 56.3 divided by each of the following.
(a)56.3 / 10(1)
(b)56.3 / 100(1)
(c)56.3 / 1000(1)
(Total for Question 7 is 3 marks)
8
Work out each of the following, without using a calculator.
(a)0.6 x 0.7(1)
(b)1.2 x 0.3(1)
(c)2.5 x 0.04(1)
(Total for Question 8 is 3 marks)
9
Work out each of the following, without using a calculator.
(a)8.4 / 4(1)
(b)12.6 / 6(1)
(c)0.72 / 8(1)
(Total for Question 9 is 3 marks)
10
Convert each fraction to a decimal.
(a)3/4(1)
(b)7/20(1)
(c)9/25(1)
(Total for Question 10 is 3 marks)
11
Convert each decimal to a fraction in its simplest form.
(a)0.35(1)
(b)0.125(1)
(c)0.6(1)
(Total for Question 11 is 3 marks)
12
Priya buys a notebook costing £2.35, a pen costing £0.89 and a ruler costing £1.20. She pays with a £10 note.
(a)Calculate the total cost of the three items.(2)
(b)Calculate her change from £10.(2)
(Total for Question 12 is 4 marks)
13
A cyclist rides 4.65 km on Monday, 3.8 km on Tuesday and 5.05 km on Wednesday.
(a)Calculate the total distance she cycled over the three days.(2)
(b)Calculate how much further she cycled on Wednesday than on Tuesday.(1)
(Total for Question 13 is 3 marks)
14
Apples cost £1.85 per kilogram. Tom buys 2.4 kg of apples and pays with a £5 note.
(a)Calculate the total cost of the apples.(2)
(b)Calculate his change from £5.(2)
(Total for Question 14 is 4 marks)
15
Work out the value of each expression, following the correct order of operations.
(a)3.6 + 2.4 x 0.5(2)
(b)(3.6 - 1.2) / 4(2)
(Total for Question 15 is 4 marks)
16
This question is about the decimal 0.375.
(a)Show that 0.375 is equivalent to 3/8.(2)
(b)Hence write 5.375 as a mixed number in its simplest form.(2)
(Total for Question 16 is 4 marks)
17
A recipe needs 0.35 kg of flour, 0.125 kg of sugar and 0.6 kg of butter. Grace has a 1 kg bag of flour, a 0.5 kg bag of sugar and a 1 kg block of butter.
(a)Calculate the total mass of flour, sugar and butter needed for the recipe.(2)
(b)State, with a reason, whether Grace has enough of all three ingredients.(2)
(Total for Question 17 is 4 marks)
18
A car's fuel tank holds 42.5 litres of petrol when full. Petrol costs £1.46 per litre. James starts with a full tank and after a long journey has 12.8 litres of petrol left.
(a)Calculate how much petrol James used on the journey.(2)
(b)Calculate the cost of the petrol he used, giving your answer to the nearest penny.(3)
(Total for Question 18 is 5 marks)
19
In the calculation 4.n8 x 2 = 9.76, the letter n represents a single missing digit. Find the value of n, showing your working.
(Total for Question 19 is 4 marks)
20
Without using a calculator, work out which is greater, 0.6 x 0.6 or 0.6 + 0.6, and give a reason for your answer.
(Total for Question 20 is 4 marks)
Mark scheme · EP.M4 Decimals
Question 1
(a) B1 0.6 oe six tenths
(a) Answer: 0.6
(b) B1 0.06 oe six hundredths
(b) Answer: 0.06
(c) B1 0.006 oe six thousandths
(c) Answer: 0.006
Question 2
M1 all four numbers written to the same number of decimal places for comparison, e.g. 0.450, 0.454, 0.500, 0.505
A1 0.45, 0.454, 0.5, 0.505 cao
Answer: 0.45, 0.454, 0.5, 0.505
Question 3
B1 B cao
Answer: B) 0.6
Question 4
(a) B1 5.9 cao
(a) Answer: 5.9
(b) B1 6 cao
(b) Answer: 6
Question 5
(a) M1 decimal points correctly aligned, e.g. 3.45 + 2.80
(a) A1 6.25 cao
(a) Answer: 6.25
(b) M1 decimal points correctly aligned, e.g. 7.60 - 2.85
(b) A1 4.75 cao
(b) Answer: 4.75
(c) M1 decimal points correctly aligned, e.g. 5.090 + 1.351
(c) A1 6.441 cao
(c) Answer: 6.441
Question 6
(a) B1 4.82 cao
(a) Answer: 4.82
(b) B1 48.2 cao
(b) Answer: 48.2
(c) B1 482 cao
(c) Answer: 482
Question 7
(a) B1 5.63 cao
(a) Answer: 5.63
(b) B1 0.563 cao
(b) Answer: 0.563
(c) B1 0.0563 cao
(c) Answer: 0.0563
Question 8
(a) B1 0.42 cao
(a) Answer: 0.42
(b) B1 0.36 cao
(b) Answer: 0.36
(c) B1 0.1 cao oe 0.10
(c) Answer: 0.1
Question 9
(a) B1 2.1 cao
(a) Answer: 2.1
(b) B1 2.1 cao
(b) Answer: 2.1
(c) B1 0.09 cao
(c) Answer: 0.09
Question 10
(a) B1 0.75 cao
(a) Answer: 0.75
(b) B1 0.35 cao
(b) Answer: 0.35
(c) B1 0.36 cao
(c) Answer: 0.36
Question 11
(a) B1 7/20 cao
(a) Answer: 7/20
(b) B1 1/8 cao
(b) Answer: 1/8
(c) B1 3/5 cao
(c) Answer: 3/5
Question 12
(a) M1 2.35 + 0.89 + 1.20 seen, or a correct part sum
(a) A1 £4.44 cao
(a) Answer: £4.44
(b) M1 10 - 4.44 seen, ft from part (a)
(b) A1 £5.56 cao
(b) Answer: £5.56
Question 13
(a) M1 4.65 + 3.8 + 5.05 seen, or a correct part sum
(a) A1 13.5 km cao
(a) Answer: 13.5 km
(b) B1 1.25 km cao
(b) Answer: 1.25 km
Question 14
(a) M1 1.85 x 2.4 seen, or a correct method e.g. 1.85 x 2 + 1.85 x 0.4
(a) A1 £4.44 cao
(a) Answer: £4.44
(b) M1 5.00 - 4.44 seen, ft from part (a)
(b) A1 £0.56 cao
(b) Answer: £0.56
Question 15
(a) M1 2.4 x 0.5 = 1.2 evaluated first
(a) A1 4.8 cao
(a) Answer: 4.8
(b) M1 3.6 - 1.2 = 2.4 evaluated first
(b) A1 0.6 cao
(b) Answer: 0.6
Question 16
(a) M1 0.375 written as 375/1000 oe
(a) A1 correctly simplified to 3/8 cso, answer given so working must be shown
(a) Answer: 3/8 (shown)
(b) M1 5.375 split as 5 + 0.375, ft from part (a)
(b) A1 5 3/8 cao
(b) Answer: 5 3/8
Question 17
(a) M1 0.35 + 0.125 + 0.6 seen, or a correct part sum
(a) A1 1.075 kg cao
(a) Answer: 1.075 kg
(b) B1 correct conclusion: yes, she has enough of all three ingredients
(b) B1 valid supporting reason comparing each amount needed with the amount available, e.g. 0.35 < 1, 0.125 < 0.5 and 0.6 < 1
(b) Answer: Yes, she has enough of all three ingredients
Question 18
(a) M1 42.5 - 12.8 seen
(a) A1 29.7 litres cao
(a) Answer: 29.7 litres
(b) M1 29.7 x 1.46 seen, ft from part (a)
(b) M1 correct method to evaluate the product, e.g. 29.7 x 1 + 29.7 x 0.4 + 29.7 x 0.06
(b) A1 £43.36 awrt, from 43.362
(b) Answer: £43.36
Question 19
M1 9.76 / 2 seen
A1 4.88 found
M1 4.88 compared digit by digit with 4.n8 to identify the tenths digit
A1 n = 8 cao
Answer: n = 8
Question 20
M1 0.6 x 0.6 = 0.36 evaluated correctly
M1 0.6 + 0.6 = 1.2 evaluated correctly
A1 correct conclusion that 0.6 + 0.6 is greater
B1 valid general reason, e.g. multiplying two positive decimals that are each less than 1 gives an answer smaller than either number, whereas adding two positive numbers always gives a larger result, ft from the two calculated values
Answer: 0.6 + 0.6 = 1.2 is greater than 0.6 x 0.6 = 0.36