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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 7 300 000 in standard form. [2 marks]

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    Model answer

    The decimal point moves 6 places left, so \(7.3 \times 10^6\).

    Mark scheme

    • 7.3 seen — M1
    • \(7.3 \times 10^6\) — A1
  2. 2 Write [2 marks]

    Write \(4.1 \times 10^{-2}\) as an ordinary number. [2 marks]

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    Model answer

    Move the decimal point 2 places right: 0.041.

    Mark scheme

    • Moves the decimal point 2 places — M1
    • 0.041 — A1
  3. 3 Explain [2 marks]

    Which is bigger, \(6 \times 10^{-3}\) or \(2 \times 10^{-2}\)? Give a reason. [2 marks]

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    Model answer

    \(2 \times 10^{-2} = 0.02\) and \(6 \times 10^{-3} = 0.006\), so \(2 \times 10^{-2}\) is bigger, because \(-2\) is greater than \(-3\).

    Mark scheme

    • \(2 \times 10^{-2}\) — B1
    • A correct reason — Q1
  4. 4 Write [3 marks]

    (a) Write 0.00086 in standard form. [2 marks] (b) Write \(2.5 \times 10^4\) as an ordinary number. [1 mark]

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    Model answer

    (a) The point moves 4 places right, so \(8.6 \times 10^{-4}\). (b) 25 000.

    Mark scheme

    • (a) 8.6 seen — M1
    • (a) \(8.6 \times 10^{-4}\) — A1
    • (b) 25 000 — B1
  5. 5 Write [2 marks]

    Write \(0.8 \times 10^5\) in standard form. [2 marks]

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    Model answer

    \(0.8 = 8 \times 10^{-1}\), so \(0.8 \times 10^5 = 8 \times 10^4\).

    Mark scheme

    • \(80\,000\) or \(8 \times 10^{-1}\) seen — M1
    • \(8 \times 10^4\) — A1
  6. 6 Work out [3 marks]

    A virus is 0.00000012 m long. [3 marks] (a) Write this length in standard form. [2 marks] (b) A bacterium is \(3 \times 10^{-6}\) m long. Which is longer, the virus or the bacterium? [1 mark]

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    Model answer

    (a) The point moves 7 places right, so \(1.2 \times 10^{-7}\) m. (b) \(3 \times 10^{-6}\) is bigger than \(1.2 \times 10^{-7}\), so the bacterium is longer.

    Mark scheme

    • (a) 1.2 seen — M1
    • (a) \(1.2 \times 10^{-7}\) — A1
    • (b) The bacterium — 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 \(8 \times 10^{-5} = 0.00008\).