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Standard form – GCSE Maths

Foundation and Higher · Grade 5

Jump to the questions and answers · Download the worksheet (PDF)

Write very large or very small numbers as and calculate with them, keeping the answer in standard form. It is on Foundation and Higher, aimed at grade 5. Free questions with answers are on this page. Worked examples show each line before you try the questions.

Standard form is with and an integer. Multiply: multiply the s and add the indices. Divide: divide the s and subtract the indices. Then tidy so is back in range: . Adding and subtracting need the same power of first.

Calculator: the key, not typed as ordinary digits with a missing bracket. Non-calculator: write the law of indices you used. Answers must be in standard form unless the question asks for an ordinary number.

Multiply/divide the numbers and add/subtract the powers separately, then adjust so the number part is from 1 up to but not including 10. Addition needs the same power of 10 first. Non-calc standard form is a 2-mark staple.

Objectives

Key points

Worked examples

Example 1

Work out (3×10^4)×(2×10^3). Give your answer in standard form.

2 marks

  1. Group fronts and powers: (3 × 2) × (10^4 × 10^3).
  2. Multiply fronts: 3 × 2 = 6, and add powers: 4 + 3 = 7.
  3. The product is 6×10^7.

Answer: 6×10^7

Common slips
  • Slip: Add front numbers 3 + 2. Front numbers multiply while powers of 10 add.
  • Slip: Brian added fronts to get 5 × 10^7. Front factors multiply together.
  • Slip: Conclude 5×10^7. Combining 6 and 10^7 gives 6×10^7.

Example 2

Work out (8×10^6)÷(2×10^2). Give your answer in standard form.

2 marks

  1. Group fronts and powers: (8 / 2) × (10^6 / 10^2).
  2. Divide fronts: 8 / 2 = 4, and subtract powers: 6 - 2 = 4.
  3. The quotient is 4×10^4.

Answer: 4×10^4

Common slips
  • Slip: Divide fronts and add powers. In division, powers of 10 subtract.
  • Slip: Clara added powers to get 4 × 10^8. Division of index terms subtracts the powers.
  • Slip: Conclude 4×10^8. Combining 4 and 10^4 gives 4×10^4.

Example 3

Write 3400 in standard form.

3 marks

  1. Place decimal point after the first non-zero digit: 3.4.
  2. Count moves to restore original: 3 places to the right, so power is 3.
  3. The standard form is 3.4×10^3.

Answer: 3.4×10^3

Common slips
  • Slip: Keep 34 as the front number. The front number A must satisfy 1 ≤ A < 10.
  • Slip: David wrote 34 × 10^2. 34 is not between 1 and 10.
  • Slip: Conclude 34×10^2. 3.4 × 10^3 equals 3400.

Questions and answers

GCSE Maths standard form questions and answers. Try each one, then open the answer. Easy questions come first.

Question 1 Easy2 marks

Work out (4×10^2)×(3×10^3). Give your answer in standard form.

Show answer

Answer: 1.2×10^6

  1. Multiply fronts: 4 × 3 = 12, powers: 2 + 3 = 5.
  2. Adjust to standard form: 12 × 10^5 = 1.2×10^6.
  • M1 — Multiply fronts: 4 × 3 = 12, powers: 2 + 3 = 5.
  • A1 — Adjust to standard form: 12 × 10^5 = 1.2×10^6.

Question 2 Easy2 marks

Work out (2×10^5)×(4×10^1). Give your answer in standard form.

Show answer

Answer: 8×10^6

  1. Multiply fronts: 2 × 4 = 8.
  2. Add powers: 5 + 1 = 6, giving 8×10^6.
  • M1 — Multiply fronts: 2 × 4 = 8.
  • A1 — Add powers: 5 + 1 = 6, giving 8×10^6.

Question 3 Medium2 marks

Work out (8×10^6)÷(4×10^2). Give your answer in standard form.

Show answer

Answer: 2×10^4

  1. Divide fronts: 8 / 4 = 2.
  2. Subtract powers: 6 - 2 = 4, giving 2×10^4.
  • M1 — Divide fronts: 8 / 4 = 2.
  • A1 — Subtract powers: 6 - 2 = 4, giving 2×10^4.

Question 4 Medium2 marks

Work out (9×10^7)÷(3×10^2). Give your answer in standard form.

Show answer

Answer: 3×10^5

  1. Divide fronts: 9 / 3 = 3.
  2. Subtract powers: 7 - 2 = 5, giving 3×10^5.
  • M1 — Divide fronts: 9 / 3 = 3.
  • A1 — Subtract powers: 7 - 2 = 5, giving 3×10^5.

Question 5 Hard2 marks

Write 52000 in standard form.

Show answer

Answer: 5.2×10^4

  1. Place decimal: 5.2.
  2. Count moves: 4 places, so 5.2×10^4.
  • M1 — Place decimal: 5.2.
  • A1 — Count moves: 4 places, so 5.2×10^4.

Question 6 Hard2 marks

Write 25000 in standard form.

Show answer

Answer: 2.5×10^4

  1. Place decimal: 2.5.
  2. Count moves: 4 places right, so 2.5×10^4.
  • M1 — Place decimal: 2.5.
  • A1 — Count moves: 4 places right, so 2.5×10^4.

Question 7 Exam-style2 marks

Work out (8×10^8)÷(2×10^3). Give your answer in standard form.

Show answer

Answer: 4×10^5

  1. Divide the front numbers: 8 / 2 = 4.
  2. Subtract powers of 10: 8 - 3 = 5, giving 4×10^5.
  • M1 — 8 ÷ 2 = 4, or 8 − 3 = 5 for the power
  • A1 — 4×10^5

Common mistakes

Most lost marks on this topic are one slip.

  1. Adding the front numbers when multiplying

    Multiply the fronts and add the powers

  2. Adding the powers when dividing

    Subtract the powers

  3. Leaving a front number of 10 or more

    Adjust so the front is below 10

Spot the slip

Ada multiplies (3×10^4)×(2×10^3) and adds the front numbers only. What is the product?

  1. 6×10^7
  2. 5×10^7
  3. 6×10^12
Show the slip

6×10^7 3×2 = 6 and powers add: 4+3 = 7, giving 6×10^7.

Exam tips

Printable worksheet

The same questions are in a PDF you can print. Answers start on a later page.

Download worksheet (PDF)

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Questions students ask

Is Standard form Foundation or Higher?

Standard form is on Foundation and Higher, aimed at grade 5.

What is a common slip on Standard form?

Adding the front numbers when multiplying. Multiply the fronts and add the powers.

Where can I get Standard form questions and answers?

The questions on this page are free. Open Show answer under each one, or download the worksheet PDF. Start free to practise this topic in the app.

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Last updated 9 November 2026.

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