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Exam questions · Maths · Standard Form and Accuracy

Calculating with Standard Form

  • 6 exam questions
  • 16 marks
  • 9 quick checks
  1. 1 Work out [2 marks]

    Work out \((2 \times 10^3) \times (3 \times 10^4)\). Give your answer in standard form.

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    Model answer

    \(2 \times 3 = 6\) and \(10^3 \times 10^4 = 10^7\), so the answer is \(6 \times 10^7\).

    Mark scheme

    • \(2 \times 3\) or \(10^{3 + 4}\) — M1
    • \(6 \times 10^7\) — A1
  2. 2 Work out [2 marks]

    Work out \((6 \times 10^8) \div (3 \times 10^3)\). Give your answer in standard form.

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    Model answer

    \(6 \div 3 = 2\) and \(10^8 \div 10^3 = 10^5\), so the answer is \(2 \times 10^5\).

    Mark scheme

    • \(6 \div 3\) or \(10^{8 - 3}\) — M1
    • \(2 \times 10^5\) — A1
  3. 3 Work out [3 marks]

    Work out \((4 \times 10^5) \times (5 \times 10^3)\). Give your answer in standard form.

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    Model answer

    \(4 \times 5 = 20\) and \(10^5 \times 10^3 = 10^8\), giving \(20 \times 10^8\). In standard form this is \(2 \times 10^9\).

    Mark scheme

    • \(20 \times 10^8\) — M1
    • Adjusts to standard form — M1
    • \(2 \times 10^9\) — A1
  4. 4 Work out [3 marks]

    Work out \(3 \times 10^4 + 5 \times 10^3\). Give your answer in standard form.

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    Model answer

    \(3 \times 10^4 = 30\,000\) and \(5 \times 10^3 = 5000\), so the total is \(35\,000 = 3.5 \times 10^4\).

    Mark scheme

    • Both numbers written with the same power, or as ordinary numbers — M1
    • 35 000 or \(3.5 \times 10^4\) seen — M1
    • \(3.5 \times 10^4\) — A1
  5. 5 Work out [3 marks]

    A bacterium is \(2 \times 10^{-6}\) m long. \(5 \times 10^8\) of these bacteria are put end to end in a line. Work out the length of the line. Give your answer in standard form.

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    Model answer

    \((5 \times 10^8) \times (2 \times 10^{-6}) = 10 \times 10^2 = 1 \times 10^3\) m.

    Mark scheme

    • \(5 \times 2 = 10\) or \(10^8 \times 10^{-6} = 10^2\) — M1
    • \(10 \times 10^2\) — M1
    • \(1 \times 10^3\) m — A1
  6. 6 Work out [3 marks]

    Work out \((3.6 \times 10^7) \div (1.2 \times 10^{-2})\). Give your answer in standard form.

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    Model answer

    \(3.6 \div 1.2 = 3\), and \(10^7 \div 10^{-2} = 10^{7 - (-2)} = 10^9\). The answer is \(3 \times 10^9\).

    Mark scheme

    • \(3.6 \div 1.2 = 3\) — M1
    • \(10^9\) seen — M1
    • \(3 \times 10^9\) — A1

Quick check

  1. 1

    What is \((2 \times 10^3) \times (3 \times 10^4)\)?

    1. A\(6 \times 10^{12}\)
    2. B\(5 \times 10^7\)
    3. C\(6 \times 10^7\)
    4. D\(6 \times 10^1\)
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    C: \(6 \times 10^7\)

    Multiply \(2 \times 3 = 6\) and add the powers, \(3 + 4 = 7\).

  2. 2

    What is \((6 \times 10^8) \div (3 \times 10^3)\)?

    1. A\(2 \times 10^{11}\)
    2. B\(2 \times 10^5\)
    3. C\(3 \times 10^5\)
    4. D\(2 \times 10^{8}\)
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    B: \(2 \times 10^5\)

    Divide \(6 \div 3 = 2\) and subtract the powers, \(8 - 3 = 5\).

  3. 3

    What is \((4 \times 10^5) \times (5 \times 10^3)\) in standard form?

    1. A\(2 \times 10^9\)
    2. B\(20 \times 10^8\)
    3. C\(2 \times 10^8\)
    4. D\(9 \times 10^8\)
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    A: \(2 \times 10^9\)

    \(4 \times 5 = 20\) and \(10^5 \times 10^3 = 10^8\), so \(20 \times 10^8 = 2 \times 10^9\).

  4. 4

    What is \(3 \times 10^4 + 5 \times 10^3\) in standard form?

    1. A\(8 \times 10^4\)
    2. B\(8 \times 10^7\)
    3. C\(3.5 \times 10^3\)
    4. D\(3.5 \times 10^4\)
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    D: \(3.5 \times 10^4\)

    \(30\,000 + 5000 = 35\,000 = 3.5 \times 10^4\).

  5. 5

    What is \(6.2 \times 10^5 - 3 \times 10^4\) in standard form?

    1. A\(3.2 \times 10^1\)
    2. B\(5.9 \times 10^4\)
    3. C\(5.9 \times 10^5\)
    4. D\(3.2 \times 10^5\)
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    C: \(5.9 \times 10^5\)

    \(620\,000 - 30\,000 = 590\,000 = 5.9 \times 10^5\).

  6. 6

    What is \(10^7 \div 10^{-2}\)?

    1. A\(10^5\)
    2. B\(10^9\)
    3. C\(10^{-5}\)
    4. D\(10^{-9}\)
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    B: \(10^9\)

    Subtract the powers: \(7 - (-2) = 9\).

  7. 7

    What is \((4 \times 10^{-3}) \times (2 \times 10^{-2})\)?

    1. A\(8 \times 10^{-5}\)
    2. B\(8 \times 10^{-6}\)
    3. C\(6 \times 10^{-5}\)
    4. D\(8 \times 10^{5}\)
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    A: \(8 \times 10^{-5}\)

    Multiply \(4 \times 2 = 8\) and add the powers, \(-3 + (-2) = -5\).

  8. 8

    What is \((3.6 \times 10^7) \div (1.2 \times 10^{-2})\)?

    1. A\(3 \times 10^5\)
    2. B\(3 \times 10^{-9}\)
    3. C\(4.8 \times 10^5\)
    4. D\(3 \times 10^9\)
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    D: \(3 \times 10^9\)

    \(3.6 \div 1.2 = 3\) and \(10^7 \div 10^{-2} = 10^9\).

  9. 9

    \(5 \times 10^8\) bacteria, each \(2 \times 10^{-6}\) m long, are placed end to end. How long is the line?

    1. A\(1 \times 10^2\) m
    2. B\(10 \times 10^2\) m
    3. C\(1 \times 10^3\) m
    4. D\(1 \times 10^{14}\) m
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    C: \(1 \times 10^3\) m

    \(5 \times 2 = 10\) and \(10^8 \times 10^{-6} = 10^2\), so \(10 \times 10^2 = 1 \times 10^3\).