Work out (2 x 103) x (4 x 105). Give your answer in standard form.
(2)
10
Work out (9 x 107) / (3 x 102). Give your answer in standard form.
(2)
11
Work out (5 x 10-3) x (6 x 106). Give your answer in standard form.
(2)
12
Work out (8.4 x 104) / (2 x 10-1). Give your answer in standard form.
(2)
13
Order these numbers from smallest to largest: 6.1 x 10-2, 0.0075, 5.9 x 10-3.
(2)
14
State whether 3.4 x 100 is greater than, equal to, or less than 1. Give a reason.
(2)
15
The mass of one grain of a fine powder is 3.6 x 10-22 kg. Find the total mass of 4 x 105 grains. Give your answer in standard form.
(3)
16
A satellite signal travels 5.4 x 1011 metres in 3.0 x 106 seconds. Find its average speed in metres per second. Give your answer in standard form.
(3)
17
Simplify (2.6 x 107) + (9.4 x 106). Give your answer in standard form.
(3)
18
A bacteria colony has 4.5 x 106 cells at 9am. By 5pm it has grown to 5.4 x 107 cells. Find the factor by which the colony grew. Give your answer in standard form.
(3)
19
A sheet of card has thickness 9.0 x 10-5 metres. A pack contains 500 sheets.
(a)Find the thickness of the whole pack in metres. Give your answer in standard form.(2)
(b)Given that 1 metre = 100 centimetres, convert the thickness of the pack to centimetres. Give your answer in standard form.(2)
20
The population of Town A is 3.2 x 105. The population of Town B is 8.5 x 104. Find the difference between the two populations. Give your answer in standard form to 2 significant figures.
(4)
Mark scheme · KS3.M-N13D Standard Form: Fluency and Exam Drill
Question 1
B1 5.2 x 104 cao
Answer: 5.2 x 104
Question 2
B1 6.7 x 10-3 cao
Answer: 6.7 x 10-3
Question 3
B1 9.1 x 105 cao
Answer: 9.1 x 105
Question 4
B1 3.8 x 10-4 cao
Answer: 3.8 x 10-4
Question 5
B1 8300 cao
Answer: 8300
Question 6
B1 0.00056 cao
Answer: 0.00056
Question 7
B1 204000 cao
Answer: 204000
Question 8
B1 0.075 cao
Answer: 0.075
Question 9
M1 multiply coefficients and add powers: 2 x 4 = 8 and 103 x 105 = 108
A1 8 x 108 cao
Answer: 8 x 108
Question 10
M1 divide coefficients and subtract powers: 9 / 3 = 3 and 107-2 = 105
A1 3 x 105 cao
Answer: 3 x 105
Question 11
M1 multiply coefficients and add powers: 5 x 6 = 30 and 10-3 x 106 = 103, giving 30 x 103
A1 3 x 104 cao
Answer: 3 x 104
Question 12
M1 divide coefficients and subtract powers: 8.4 / 2 = 4.2 and 104-(-1) = 105
A1 4.2 x 105 cao
Answer: 4.2 x 105
Question 13
M1 convert to the same form or decimals, e.g. 6.1 x 10-2 = 0.061, 5.9 x 10-3 = 0.0059
A1 correct order: 5.9 x 10-3, 0.0075, 6.1 x 10-2 cao
Answer: 5.9 x 10-3, 0.0075, 6.1 x 10-2
Question 14
M1 evaluate 3.4 x 100 = 3.4 (100 = 1)
A1 correct conclusion: greater than 1, because 3.4 x 100 = 3.4 cao
Answer: Greater than 1, because 3.4 x 100 = 3.4
Question 15
M1 multiply coefficients and add powers: 3.6 x 4 = 14.4 and 10-22 x 105 = 10-17
M1 convert 14.4 x 10-17 into standard form: 1.44 x 10-16
A1 1.44 x 10-16 kg cao
Answer: 1.44 x 10-16 kg
Question 16
M1 set up division: distance / time = (5.4 x 1011) / (3.0 x 106)
M1 divide coefficients and subtract powers: 5.4 / 3.0 = 1.8 and 1011-6 = 105
A1 1.8 x 105 m/s cao
Answer: 1.8 x 105 m/s
Question 17
M1 write 9.4 x 106 with a matching power of ten, e.g. 0.94 x 107
M1 add coefficients: 2.6 + 0.94 = 3.54
A1 3.54 x 107 cao
Answer: 3.54 x 107
Question 18
M1 set up division: (5.4 x 107) / (4.5 x 106)
M1 divide coefficients and subtract powers: 5.4 / 4.5 = 1.2 and 107-6 = 101
A1 1.2 x 101 (12) cao
Answer: 1.2 x 101 (a growth factor of 12)
Question 19
(a) M1 multiply coefficients and powers: 9.0 x 10-5 x 5 x 102 (500 = 5 x 102)
(a) A1 4.5 x 10-2 m cao
(a) Answer: 4.5 x 10-2 m
(b) M1 multiply the answer to part (a) by 100 (102)
(b) A1 4.5 x 100 cm (4.5 cm) cao
(b) Answer: 4.5 x 100 cm (4.5 cm)
Question 20
M1 convert both numbers to the same power of ten or to ordinary numbers: 3.2 x 105 = 320000, 8.5 x 104 = 85000
M1 subtract correctly: 320000 - 85000 = 235000
M1 write 235000 in standard form: 2.35 x 105
A1 2.4 x 105 cao, rounded to 2 significant figures