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Exam questions · Maths · Standard Form and Accuracy

Standard Form

  • 6 exam questions
  • 14 marks
  • 9 quick checks
  1. 1 Write [2 marks]

    Write 45 000 in standard form.

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    Model answer

    The decimal point moves 4 places left, so \(45\,000 = 4.5 \times 10^4\).

    Mark scheme

    • 4.5 seen — M1
    • \(4.5 \times 10^4\) — A1
  2. 2 Write [2 marks]

    Write \(3.2 \times 10^{-3}\) as an ordinary number.

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    Model answer

    A power of \(-3\) means the decimal point moves 3 places to the right, giving \(0.0032\).

    Mark scheme

    • Moves the decimal point 3 places — M1
    • 0.0032 — A1
  3. 3 Write [2 marks]

    Write these numbers in order of size. Start with the smallest. \(3.4 \times 10^5\) \(2.9 \times 10^6\) \(8.7 \times 10^4\)

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    Model answer

    Compare the powers: 4 is the smallest, then 5, then 6. The order is \(8.7 \times 10^4\), \(3.4 \times 10^5\), \(2.9 \times 10^6\).

    Mark scheme

    • Compares the powers of 10 — M1
    • \(8.7 \times 10^4\), \(3.4 \times 10^5\), \(2.9 \times 10^6\) — A1
  4. 4 Write [3 marks]

    (a) The distance from the Earth to the Sun is 150 million kilometres. Write this distance in standard form. (1 mark) (b) A cell has a width of 0.0000052 m. Write this width in standard form. (2 marks)

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    Model answer

    (a) \(150\,000\,000 = 1.5 \times 10^8\) km. (b) The point moves 6 places right to give 5.2, so the width is \(5.2 \times 10^{-6}\) m.

    Mark scheme

    • (a) \(1.5 \times 10^8\) — B1
    • (b) 5.2 seen — M1
    • (b) \(5.2 \times 10^{-6}\) — A1
  5. 5 Explain [2 marks]

    Ravi writes the number 45 000 as \(45 \times 10^3\). Explain why this is not in standard form, and write the number correctly.

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    Model answer

    In standard form the first number must be at least 1 and less than 10. 45 is not, so the number is \(4.5 \times 10^4\).

    Mark scheme

    • 45 is not between 1 and 10 — C1
    • \(4.5 \times 10^4\) — B1
  6. 6 Work out [3 marks]

    \(N = 7.2 \times 10^5\). Write each of these in standard form. (a) \(10N\) (1 mark) (b) \(N \div 1000\) (1 mark) (c) Write \(N\) as an ordinary number. (1 mark)

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    Model answer

    (a) \(7.2 \times 10^6\). (b) \(7.2 \times 10^2\). (c) \(720\,000\).

    Mark scheme

    • (a) \(7.2 \times 10^6\) — B1
    • (b) \(7.2 \times 10^2\) — B1
    • (c) 720 000 — B1

Quick check

  1. 1

    What is 45 000 in standard form?

    1. A\(45 \times 10^3\)
    2. B\(4.5 \times 10^4\)
    3. C\(4.5 \times 10^3\)
    4. D\(0.45 \times 10^5\)
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    B: \(4.5 \times 10^4\)

    The decimal point moves 4 places left to give 4.5.

  2. 2

    What is \(3.2 \times 10^{-3}\) as an ordinary number?

    1. A0.0032
    2. B0.032
    3. C3200
    4. D0.00032
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    A: 0.0032

    A power of \(-3\) moves the decimal point 3 places to the right of the 3, giving 0.0032.

  3. 3

    Which of these is in standard form?

    1. A\(62 \times 10^4\)
    2. B\(0.62 \times 10^6\)
    3. C\(6.2 \times 5^{10}\)
    4. D\(6.2 \times 10^5\)
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    D: \(6.2 \times 10^5\)

    The first part must be at least 1 and less than 10, and the base must be 10.

  4. 4

    What is 0.00045 in standard form?

    1. A\(4.5 \times 10^{4}\)
    2. B\(4.5 \times 10^{-3}\)
    3. C\(4.5 \times 10^{-4}\)
    4. D\(45 \times 10^{-5}\)
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    C: \(4.5 \times 10^{-4}\)

    The decimal point moves 4 places right, so the power is \(-4\).

  5. 5

    What is \(45 \times 10^3\) in standard form?

    1. A\(4.5 \times 10^3\)
    2. B\(4.5 \times 10^4\)
    3. C\(4.5 \times 10^2\)
    4. D\(450 \times 10^2\)
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    B: \(4.5 \times 10^4\)

    \(45 = 4.5 \times 10\), so \(45 \times 10^3 = 4.5 \times 10^4\).

  6. 6

    Which is bigger, \(2 \times 10^7\) or \(9 \times 10^6\)?

    1. A\(2 \times 10^7\)
    2. B\(9 \times 10^6\)
    3. CThey are equal
    4. DIt cannot be worked out
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    A: \(2 \times 10^7\)

    \(2 \times 10^7 = 20\,000\,000\) and \(9 \times 10^6 = 9\,000\,000\).

  7. 7

    The distance to the Sun is about 150 million km. What is this in standard form?

    1. A\(1.5 \times 10^6\) km
    2. B\(15 \times 10^7\) km
    3. C\(1.5 \times 10^9\) km
    4. D\(1.5 \times 10^8\) km
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    D: \(1.5 \times 10^8\) km

    150 million is 150 000 000, so the point moves 8 places to give 1.5.

  8. 8

    What is \(3.2 \times 10^5\) as an ordinary number?

    1. A32 000
    2. B3 200 000
    3. C320 000
    4. D0.000032
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    C: 320 000

    Move the decimal point 5 places right.

  9. 9

    Which is smaller, \(5 \times 10^{-3}\) or \(8 \times 10^{-5}\)?

    1. A\(5 \times 10^{-3}\)
    2. B\(8 \times 10^{-5}\)
    3. CThey are equal
    4. DIt depends on the first part
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    B: \(8 \times 10^{-5}\)

    \(5 \times 10^{-3} = 0.005\) and \(8 \times 10^{-5} = 0.00008\).