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Grade 4 · Foundation and Higher · free GCSE maths worksheet

Writing numbers in standard form

Converting large and small numbers to and from a x 10^n.

11 original questions, 23 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
  1. Write 8.14 × 104 as an ordinary number.
  2. Write 0.00092 in standard form.
2 marks
Show answer
a) 81,400 b) 9.2 x 10-4
2

Write 45 000 000 in standard form.

1 mark
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4.5 × 107
3

Write 0.00032 in standard form.

1 mark
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3.2 × 10-4
4
  1. Write 507,000 in standard form.
  2. Write 2.6 × 10−3 as an ordinary number.
2 marks
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a) 5.07 x 105 b) 0.0026
5

Ravi writes 56 000 as 56 × 103.

Is this in standard form? Give a reason, and write 56 000 correctly in standard form.

2 marks
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No, 56 is not between 1 and 10. 5.6 x 104
6

Write each number in standard form.

  1. 830 000
  2. 0.0705
2 marks
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a) 8.3 x 105 b) 7.05 x 10-2
7

Here are four numbers.

A: 3.4 × 105    B: 0.6 × 10−2    C: 12 × 103    D: 9.99 × 10−7

Write down the letters of the numbers that are in standard form.

2 marks
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A and D
8

Write each of these in standard form.

  1. A virus is 0.00000012 m across.
  2. The population of India is about 1 400 000 000.
2 marks
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a) 1.2 x 10-7 b) 1.4 x 109
9

A grain of sand has width 2 × 10−3 m, a speck of pollen has width 1.8 × 10−4 m and a dust particle has width 5 × 10−5 m.

  1. Write the three objects in order of size, smallest first.
  2. Write the ratio of the width of the sand grain to the width of the dust particle in the form n : 1.
4 marks
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a) dust particle, pollen, sand grain b) 40 : 1
10

Write these numbers in order of size, starting with the smallest.

3.2 × 104    2.9 × 105    8.7 × 103    3.05 × 104

2 marks
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8.7 x 103, 3.05 x 104, 3.2 x 104, 2.9 x 105
11
  1. Write 0.0698 in standard form.
  2. Which is greater, 7.3 × 10−2 or 0.0698?

    You must show your working.

3 marks
Show answer
a) 6.98 x 10-2 b) 7.3 x 10-2 (0.073 > 0.0698)

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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