Robinson Tuition
Grade 5 · Foundation and Higher · free GCSE maths worksheet

Calculating with numbers in standard form

Multiplying, dividing, adding and subtracting.

15 original questions, 43 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

Worksheet PDFWorked solutions PDFAnswers PDF

The questions

1

Work out (7 × 104) × (3 × 105)

Give your answer in standard form.

2 marks
Show answer
2.1 x 1010
2

Work out (9 × 108) ÷ (3 × 10−2)

Give your answer in standard form.

2 marks
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3 x 1010
3

Work out (6.5 × 105) + (5.8 × 105)

Give your answer in standard form.

2 marks
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1.23 x 106
4

Work out (3 × 104)2

Give your answer in standard form.

2 marks
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9 x 108
5

8w = 2 × 105

Find the value of w.

Give your answer in standard form.

2 marks
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2.5 x 104
6

Work out (4.6 × 105) + (3.1 × 104)

Give your answer in standard form.

3 marks
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4.91 x 105
7

Work out (2 × 10−3)3

Give your answer in standard form.

2 marks
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8 x 10-9
8

A red blood cell has a diameter of 7 × 10−6 metres.

3 000 000 red blood cells are placed in a straight line, touching end to end.

Work out the length of the line. Give your answer in metres, in standard form.

4 marks
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2.1 x 101 m
9

The mass of the Earth is 5.97 × 1024 kg.

The mass of the Moon is 7.35 × 1022 kg.

Work out the mass of the Moon as a percentage of the mass of the Earth. Give your answer correct to 3 significant figures.

3 marks
Show answer
1.23%
10

The kinetic energy, E joules, of a moving object is given by

E = ½mv2

where m is the mass in kg and v is the speed in metres per second.

m = 4 × 10−3 and v = 6 × 102

Work out the value of E. Give your answer in standard form.

3 marks
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7.2 x 102
11

Work out (6.4 × 106) − (5.9 × 105)

Give your answer in standard form.

3 marks
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5.81 x 106
12

The population of country A is 6.85 × 107

The population of country B is 928,000

Work out the total population of the two countries.

Give your answer in standard form.

4 marks
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6.9428 x 107
13

A phone network handles 3.2 × 105 text messages every hour.

Work out an estimate for the number of text messages handled in 30 days. Give your answer in standard form, correct to 2 significant figures.

3 marks
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2.3 x 108
14

A grain of sand has a mass of 0.0032 grams.

A bag contains 5 × 106 grains of sand.

Work out the total mass of the sand in the bag.

Give your answer in grams, in standard form.

4 marks
Show answer
1.6 x 104 g
15

Data travels along an undersea fibre-optic cable at a speed of 2 × 105 kilometres per second.

The cable is 1.3 × 104 kilometres long.

  1. Work out the time taken for data to travel the full length of the cable.

    Give your answer in seconds, in standard form.

  2. Write your answer to part (a) in milliseconds.
4 marks
Show answer
a) 6.5 x 10-2 s b) 65 ms

Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.

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