[discia] GCSE Maths › Number › Standard Form

Standard Form

discia.org 10 questions · 25 marks
Name Date
  1. Either paper 3 marks
    (a)

    Write 490,000 in standard form.

    (b)

    Write \(1.8 \times 10^{ -2 }\) as an ordinary number.

    (c)

    Write \(0.0078\) in standard form.

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    (a) \(4.9 \times 10^{ 5 }\)
    (b) \(0.018\)
    (c) \(7.8 \times 10^{ -3 }\)
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  2. Either paper 1 mark
    Here are four numbers.
    ABCD
    \(0.1 \times 10^{ -4 }\)\(7.1 \times 10^{ 0.5 }\)\(53.8 \times 10^{ 7 }\)\(6 \times 10^{ 6 }\)
    One of the numbers is written in standard form. State the letter of that number.
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    D, \(6 \times 10^{ 6 }\)
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  3. Either paper 2 marks

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

    \(2.7 \times 10^{ -3 } \qquad 2.1 \times 10^{ -1 } \qquad 3.3 \times 10^{ 2 } \qquad 4.8 \times 10^{ -3 }\)

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    \(2.7 \times 10^{ -3 }, \; 4.8 \times 10^{ -3 }, \; 2.1 \times 10^{ -1 }, \; 3.3 \times 10^{ 2 }\)
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  4. Either paper 2 marks
    (a)

    Write \(59 \times 10^{ 7 }\) in standard form.

    (b)

    Write \(0.06 \times 10^{ -3 }\) in standard form.

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    (a) \(5.9 \times 10^{ 8 }\)
    (b) \(6 \times 10^{ -5 }\)
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  5. Either paper 4 marks
    (a)

    Work out 980 ÷ 8

    Give your answer in standard form.

    (b)

    Work out 0.05 × 4

    Give your answer in standard form.

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    (a) \(1.225 \times 10^{ 2 }\)
    (b) \(2 \times 10^{ -1 }\)
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  6. Either paper 4 marks
    (a)

    Find the value of \((6 \times 10^{ 3 }) \times (1.2 \times 10^{ -2 })\)

    Give your answer in standard form.

    (b)

    Find the value of \((3 \times 10^{ 5 }) \div (2 \times 10^{ 2 })\)

    Give your answer in standard form.

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    (a) \(7.2 \times 10^{ 1 }\)
    (b) \(1.5 \times 10^{ 3 }\)
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  7. Either paper 3 marks

    One sheet of paper is \(4.6 \times 10^{-5}\) metres thick.

    Priya stacks 7,000 identical sheets in a pile.

    Work out the height of the pile. Give your answer in standard form.

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    \(3.22 \times 10^{ -1 }\ \text{m}\)
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  8. Either paper 2 marks

    Sample A contains \(7 \times 10^{ 3 }\) bacteria.

    Sample B contains \(4.62 \times 10^{ 6 }\) bacteria.

    Work out how many times more bacteria there are in Sample B than in Sample A.

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    \(660\ \text{times}\)
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  9. Either paper 2 marks

    A bar of chocolate has a mass of 120 g.

    Write this mass in kilograms. Give your answer in standard form.

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    \(1.2 \times 10^{ -1 }\ \text{kg}\)
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  10. Either paper 2 marks

    Here are four numbers.

    \(\text{A: } 619 \qquad \text{B: } 4.1 \times 10^{ 2 } \qquad \text{C: } 53 \times 10^{ 1 } \qquad \text{D: } 6.8^{ 4 }\)

    Write the letters in order of size, starting with the smallest. You may use a calculator.

    Show answer
    B C A D
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discia.org Standard Form · sheet 1
Answers Standard Form · sheet 1
  1. (a) \(4.9 \times 10^{ 5 }\)
    (b) \(0.018\)
    (c) \(7.8 \times 10^{ -3 }\)
  2. D, \(6 \times 10^{ 6 }\)
  3. \(2.7 \times 10^{ -3 }, \; 4.8 \times 10^{ -3 }, \; 2.1 \times 10^{ -1 }, \; 3.3 \times 10^{ 2 }\)
  4. (a) \(5.9 \times 10^{ 8 }\)
    (b) \(6 \times 10^{ -5 }\)
  5. (a) \(1.225 \times 10^{ 2 }\)
    (b) \(2 \times 10^{ -1 }\)
  6. (a) \(7.2 \times 10^{ 1 }\)
    (b) \(1.5 \times 10^{ 3 }\)
  7. \(3.22 \times 10^{ -1 }\ \text{m}\)
  8. \(660\ \text{times}\)
  9. \(1.2 \times 10^{ -1 }\ \text{kg}\)
  10. B C A D
discia.org Standard Form · sheet 1