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GCSE Maths / Edexcel

Standard form

Write very large and very small numbers in standard form, convert back to ordinary numbers, and calculate with powers of 10.

Number and Place ValueFoundation and HigherGrades 4 to 7Skill

Curriculum path: GCSE Maths > Edexcel > Number > Standard form

Pearson Edexcel GCSE Maths number: use standard form A x 10ⁿ where 1 <= A < 10 and n is an integer.

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Revision notes

Theory, examples, and quick checks.

Keep the method short, then practise straight away. This note is written for GCSE Maths Edexcel students who need clear working and reliable method marks.

Theory

Standard form is a shorter way to write very large or very small numbers. It is used often in science-style GCSE questions.

A number in standard form must look like A x 10ⁿ, where A is at least 1 but less than 10. For example, 4.8 is allowed, but 48 is not allowed.

To write a large number in standard form, move the decimal point left until the first number is between 1 and 10. The number of moves becomes a positive power of 10.

To write a small decimal in standard form, move the decimal point right until the first number is between 1 and 10. The number of moves becomes a negative power of 10.

To convert back to an ordinary number, use the power of 10 as the instruction for moving the decimal point: positive powers make the number bigger, negative powers make it smaller.

For Edexcel method marks, show the number part and the power of 10 clearly. If the first number is 10 or more, adjust it back into standard form.

Key ruleStandard form: A x 10ⁿ, where 1 <= A < 10.

Worked examples

Large number

Write 480000 in standard form.

  1. Place the decimal point after the first non-zero digit: 4.8.
  2. Count how many places the decimal point moved from 480000 to 4.8: 5 places.
  3. The original number was large, so use a positive power of 10.

Answer: 4.8 x 10⁵

Small decimal

Write 0.0062 in standard form.

  1. The first useful digit is 6, so make the number part 6.2.
  2. The decimal point moved 3 places right from 0.0062 to 6.2.
  3. The original number was small, so use a negative power of 10.

Answer: 6.2 x 10⁻³

Convert back

Write 3.41 x 10⁴ as an ordinary number.

  1. 10⁴ means move the decimal point 4 places right.
  2. 3.41 becomes 34100.

Answer: 34100

Common mistakes

  • Using a first number that is not between 1 and 10.
  • Using a positive power for a very small decimal.
  • Counting the digits rather than the decimal-place moves.
  • Writing 48 x 10⁴ instead of 4.8 x 10⁵.

Quick exercise

Try these before moving to the exam-style questions.

  1. Write 720000 in standard form.
  2. Write 0.0045 in standard form.
  3. Write 6.3 x 10³ as an ordinary number.
  4. Write 2.08 x 10⁻² as an ordinary number.
  5. Write 91000000 in standard form.
Exam-style questions

Practise the same skill at three levels.

These are original GCSE-style questions with mark schemes, common wrong answers, and AI marking guidance so feedback stays close to exam expectations.

Basic GCSE styleFoundationNon-calculator2 marks

Write 5600000 in standard form.

standard formlarge numberspowers of 10
Standard exam styleFoundation and HigherEither3 marks

Work out (3 x 10⁵) x (4 x 10³). Give your answer in standard form.

standard form calculationsindex lawsstandard form correction
ChallengeHigherCalculator4 marks

The mass of one grain of sand is about 6.5 x 10⁻⁵ g. Estimate the mass of 800000 grains of sand. Give your answer in standard form.

standard form modellingnegative powersestimation