GCSE Standard form Practice Questions

Free GCSE Standard form practice questions with full step-by-step worked solutions. Covers converting to standard form, converting from standard form, ordering standard form, comparing standard form. Practise exam-style problems and check your method.

converting to standard formconverting from standard formordering standard formcomparing standard formmultiplying standard formdividing standard form
GCSE Foundation70 questionsStep-by-step solutions
Question 1
2 markseasy
Write 40004000 in standard form.
Show worked solution

Worked solution

  1. Find the significant figures

    40004000

    Ignore the zeros that are only there for place value.

  2. Write AA with one non-zero digit before the point

    A=4A = 4

    Standard form needs 11 ≤\le A<10A < 10, so the decimal point goes after the first significant figure.

  3. Count how far the point moves

    n=3n = 3

    The number is large, so the power is positive: n=3n = 3.

  4. Write it in standard form

    4×1034 \times 10^{3}

    So 4000=4×1034000 = 4 \times 10^{3}.

Answer
4×1034 \times 10^{3}
Question 2
2 markseasy
Write 99 ×\times 10510^{5} as an ordinary number.
Show worked solution

Worked solution

  1. Read the power of 1010

    10510^{5}

    The power 55 tells you how far to move the decimal point.

  2. Decide the direction

    move right\text{move right}

    A positive power moves the point right, making the number bigger.

  3. Move the decimal point

    9→9000009 \rightarrow 900000

    Move the point 55 places, filling with zeros as needed.

  4. Write the ordinary number

    900000900000

    So 99 ×\times 105=90000010^{5} = 900000.

Answer
900000900000
Question 3
3 marksintermediate
Work out (44 ×\times 10210^{2}) ×\times (2.52.5 ×\times 10310^{3}), giving your answer in standard form.
Show worked solution

Worked solution

  1. Group numbers and powers

    (4×2.5)×(102×103)(4 \times 2.5) \times (10^{2} \times 10^{3})

    Multiply the front numbers together and the powers of 1010 together.

  2. Multiply the front numbers

    4×2.5=104 \times 2.5 = 10

    Multiply the AA parts.

  3. Add the powers

    102×103=10510^{2} \times 10^{3} = 10^{5}

    When multiplying powers of 1010, add the indices.

  4. Put it together

    10×10510 \times 10^{5}

    Combine the two results.

  5. Check AA is in range

    10 is not 1≤A<1010 \text{ is not } 1 \le A < 10

    The front number is out of range, so adjust.

  6. Rewrite in proper standard form

    1×1061 \times 10^{6}

    Move the point one place and change the power to make 11 ≤\le A<10A < 10.

  7. State the answer

    1×1061 \times 10^{6}

    So the product is 11 ×\times 10610^{6}.

Answer
1×1061 \times 10^{6}
Question 4
4 markshard
Work out (77 ×\times 10−310^{-3}) ×\times (33 ×\times 10610^{6}), giving your answer in standard form.
Show worked solution

Worked solution

  1. Group numbers and powers

    (7×3)×(10−3×106)(7 \times 3) \times (10^{-3} \times 10^{6})

    Multiply the front numbers together and the powers of 1010 together.

  2. Multiply the front numbers

    7×3=217 \times 3 = 21

    Multiply the AA parts.

  3. Add the powers

    10−3×106=10310^{-3} \times 10^{6} = 10^{3}

    When multiplying powers of 1010, add the indices.

  4. Put it together

    21×10321 \times 10^{3}

    Combine the two results.

  5. Check AA is in range

    21 is not 1≤A<1021 \text{ is not } 1 \le A < 10

    The front number is out of range, so adjust.

  6. Rewrite in proper standard form

    2.1×1042.1 \times 10^{4}

    Move the point one place and change the power to make 11 ≤\le A<10A < 10.

  7. State the answer

    2.1×1042.1 \times 10^{4}

    So the product is 2.12.1 ×\times 10410^{4}.

  8. Verify by expanding

    ≈21000\approx 21000

    Working the calculation out as ordinary numbers gives the same value.

  9. Confirm the final form

    2.1×1042.1 \times 10^{4}

    The answer is in proper standard form.

  10. Interpret

    1≤2.1<101 \le 2.1 < 10

    The front number is between 11 and 1010 and the power records the size.

Answer
2.1×1042.1 \times 10^{4}
Question 5
4 markschallenging
Priya writes 0.50.5 ×\times 10610^{6} as her final answer. Explain why this is not in standard form and give the correct version.
Show worked solution

Worked solution

  1. Recall the rule

    A×10n, 1≤A<10A \times 10^{n},\ 1 \le A < 10

    The front number must be at least 11 and less than 1010.

  2. Look at the front number

    A=0.5A = 0.5

    Here AA is 0.50.5.

  3. Check the range

    0.5<10.5 < 1

    0.50.5 is less than 11, so it breaks the rule.

  4. Conclude it is not standard form

    not standard form\text{not standard form}

    So 0.50.5 x 10610^{6} is not proper standard form.

  5. Rewrite 0.50.5

    0.5=5×10−10.5 = 5 \times 10^{-1}

    Move the point one place right.

  6. Combine the powers

    5×10−1×106=5×1055 \times 10^{-1} \times 10^{6} = 5 \times 10^{5}

    Add the indices: −1+6=5-1 + 6 = 5.

  7. State the correct form

    5×1055 \times 10^{5}

    The proper standard form is 55 x 10510^{5}.

  8. Check AA is in range

    1≤5<101 \le 5 < 10

    Now the front number is in range.

  9. Confirm the value is unchanged

    500000=500000500000 = 500000

    Both forms equal 500000500000.

  10. Answer the question

    5×1055 \times 10^{5}

    So the correct version is 55 x 10510^{5}.

  11. Underline the final answer

    5×1055 \times 10^{5} (since AA must be at least 11).

    Write the answer on its own line so it is clear and easy to mark.

  12. Check it answers the question

    5×1055 \times 10^{5} (since AA must be at least 11).

    Re-reading the question, this is exactly what was required.

  13. State the conclusion in one line

    5×1055 \times 10^{5} (since AA must be at least 11).

    The working above leads directly to this result.

  14. Match to the options

    5×1055 \times 10^{5} (since AA must be at least 11).

    Compare each choice; only the option agreeing with this working is correct.

  15. Sense check

    5×1055 \times 10^{5} (since AA must be at least 11).

    The result is consistent with the checks done along the way.

Answer
5×1055 \times 10^{5} (since AA must be at least 11).

Unlock 65 more Standard form questions

Create a free account to work through every GCSE Standard form question with instant step-by-step worked solutions, progress tracking and interactive lessons.

  • Full worked solutions for every question
  • Interactive lessons and instant feedback
  • Track your mastery across every topic
Create a Free Account

No card required · Free forever

More Standard form practice

Hard QuestionsWorked Solutions

Related Number topics

Upper and lower boundsError intervalsEstimating powers and rootsEstimation and checkingExact calculationFactors, multiples and primes