Number: Standard Form and Rounding - Worksheets, Questions and Revision

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KS3 · Number

KS3.M-N3 Number: Standard Form and Rounding

AQA AQA KS3 · Calculator allowed · about 80 minutes
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
Round the number 3847 to:
(a)the nearest 10(1)
(b)the nearest 100(1)
(c)the nearest 1000(1)
2
The number 5.6789 is given.
(a)Round 5.6789 to 1 decimal place.(1)
(b)Round 5.6789 to 2 decimal places.(1)
3
The number 0.04563 is given. Round it to:
(a)1 significant figure(1)
(b)2 significant figures(1)
(c)3 significant figures(1)
4
By rounding each number to 1 significant figure, estimate the value of (398 x 5.2) / 19.8. You must show your rounded values.
(2)
5
Write these numbers in standard form:
(a)480000(1)
(b)0.00072(1)
(c)6030000(1)
6
Write these standard form numbers as ordinary numbers:
(a)3.4 x 104(1)
(b)9.05 x 10-3(1)
(c)1.2 x 107(1)
7
Standard form must have a single digit from 1 to 9 before the decimal point.
(a)Which of the following correctly represents 4500 in standard form?(1)
  • A) 45 x 102
  • B) 4.5 x 103
  • C) 0.45 x 104
  • D) 4.5 x 102
(b)Rewrite 45 x 102 correctly in standard form.(1)
8
Calculate the following, giving each answer in standard form.
(a)(2.5 x 103) x (3 x 104)(2)
(b)(6 x 105) x (4 x 10-2)(2)
9
Calculate the following, giving each answer in standard form.
(a)(8 x 107) / (2 x 103)(2)
(b)(9 x 10-2) / (3 x 105)(2)
10
In 2024 the population of the UK was approximately 68500000.
(a)Write this population in standard form.(2)
(b)The population of a small town is 3.24 x 104. Round this population to the nearest thousand, giving your answer as an ordinary number.(2)
11
Priya buys three items costing 4.65 pounds, 12.20 pounds and 7.85 pounds.
(a)Work out the total cost of the three items.(1)
(b)Round the total cost to the nearest pound.(1)
(c)Using the exact total from part a, work out how much change Priya receives from a 30 pounds note.(1)
12
A school trip needs tickets for 187 students at 8.95 pounds each, plus a coach costing 396 pounds. By rounding each value to 1 significant figure, estimate the total cost of the trip. You must show your rounded values.
(3)
13
Work out (3.2 x 105) + (4.5 x 104). Give your answer in standard form.
(3)
14
Work out (7.8 x 106) - (2.5 x 105). Give your answer in standard form.
(3)
15
Write these numbers in order, starting with the smallest: 3.6 x 104, 9.1 x 103, 4.2 x 10-2, 3.6 x 10-3
(3)
16
Consider the number 6.478.
(a)Round 6.478 to 2 decimal places.(1)
(b)The number 6.478 is truncated (not rounded) to 2 decimal places. State the truncated value and explain why it is different from your answer to part a.(2)
17
A bacterium has a width of 0.0000025 metres.
(a)Write this width in standard form.(2)
(b)4000 of these bacteria are placed end to end. Calculate the total length in metres, giving your answer in standard form.(2)
18
Light travels at a speed of 3 x 108 metres per second.
(a)Calculate how far light travels in 60 seconds. Give your answer in standard form.(2)
(b)A spacecraft is 9 x 1010 metres from Earth. Work out how many seconds it would take light to travel this distance. Give your answer as an ordinary number.(3)
19
A number, when rounded to the nearest 100, is 700.
(a)Write down the smallest number it could have been.(2)
(b)Assuming the original number is a whole number, write down the largest number it could have been.(2)
20
In 2023, a company's annual revenue was 4.6 x 109 pounds and its costs were 3.85 x 109 pounds.
(a)Calculate the company's profit. Give your answer in standard form.(2)
(b)The company has 15000 employees. Work out the profit per employee, giving your answer as an ordinary number.(2)
(c)Round the total revenue, 4.6 x 109 pounds, to 1 significant figure and explain what this rounded value tells you about the size of the company.(2)
21
The diameter of a hydrogen atom is about 1 x 10-10 metres. The diameter of the Milky Way galaxy is about 9.5 x 1020 metres.
(a)Work out how many times bigger the diameter of the galaxy is than the diameter of the atom. Give your answer in standard form.(3)
(b)Round your answer to part a to 1 significant figure and comment on whether this level of precision is reasonable, given that the original diameters were only given to 2 significant figures.(2)
22
Amara estimates the value of (612 x 0.48) / 0.099 by rounding each number to 1 significant figure. Find Amara's estimate. You must show your rounded values.
(3)
Mark scheme · KS3.M-N3 Number: Standard Form and Rounding

Question 1

Question 2

Question 3

Question 4

Question 5

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Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

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Question 17

Question 18

Question 19

Question 20

Question 21

Question 22