Standard form Worked Solutions — GCSE Maths

Fully worked, step-by-step solutions to GCSE Standard form questions. See exactly how to solve problems on converting to standard form, converting from standard form, ordering standard form, comparing standard form.

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.

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 6000060000 in standard form.

Worked solution

  1. Find the significant figures

    6000060000

    Ignore the zeros that are only there for place value.

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

    A=6A = 6

    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=4n = 4

    The number is large, so the power is positive: n=4n = 4.

  4. Write it in standard form

    6×1046 \times 10^{4}

    So 60000=6×10460000 = 6 \times 10^{4}.

Answer
6×1046 \times 10^{4}
Question 3
2 markseasy
Write 4500045000 in standard form.

Worked solution

  1. Find the significant figures

    4500045000

    Ignore the zeros that are only there for place value.

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

    A=4.5A = 4.5

    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=4n = 4

    The number is large, so the power is positive: n=4n = 4.

  4. Write it in standard form

    4.5×1044.5 \times 10^{4}

    So 45000=4.5×10445000 = 4.5 \times 10^{4}.

Answer
4.5×1044.5 \times 10^{4}
Question 4
2 markseasy
Write 320320 in standard form.

Worked solution

  1. Find the significant figures

    320320

    Ignore the zeros that are only there for place value.

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

    A=3.2A = 3.2

    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=2n = 2

    The number is large, so the power is positive: n=2n = 2.

  4. Write it in standard form

    3.2×1023.2 \times 10^{2}

    So 320=3.2×102320 = 3.2 \times 10^{2}.

Answer
3.2×1023.2 \times 10^{2}
Question 5
2 markseasy
Write 70000007000000 in standard form.

Worked solution

  1. Find the significant figures

    70000007000000

    Ignore the zeros that are only there for place value.

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

    A=7A = 7

    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=6n = 6

    The number is large, so the power is positive: n=6n = 6.

  4. Write it in standard form

    7×1067 \times 10^{6}

    So 7000000=7×1067000000 = 7 \times 10^{6}.

Answer
7×1067 \times 10^{6}

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 QuestionsPractice Questions

Related Number topics

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