AQA GCSE Mathematics Paper 1 (Foundation), June 2025: Question 20
4 marks · Medium difficulty · Short Answer
Calculate the result of two arithmetic operations involving decimals and powers of 10, giving both answers in standard form.
Practise this questionQuestion
Mark scheme
Show the mark scheme
How to answer it
Calculating and Converting with Standard Form
📋 What this question tests
This question tests your ability to carry out basic operations (division and multiplication) involving powers of 10 and decimals, and to express the final values strictly in standard form (scientific notation: A × 10n, where 1 ≤ A < 10 and n is an integer).
Part (a) • 2 Marks
Work out 0.6 ÷ 100 in Standard Form
Division by powers of 10 & small numbers
📐 Step-by-Step Calculation
- Method 1 (Decimal first):
Compute the division: 0.6 ÷ 100 = 0.006
Convert to standard form: Move the decimal point 3 places right to get a leading number between 1 and 10.
0.006 = 6 × 10⁻³ - Method 2 (Index laws):
Write both parts in index form:
0.6 = 6 × 10⁻¹ and 100 = 10²
Divide: (6 × 10⁻¹) ÷ 10² = 6 × 10⁻¹⁻² = 6 × 10⁻³
✅ Correct Answer & Mark Scheme
6 × 10⁻³
B2: Full marks for 6 × 10⁻³ (condone equivalent trailing zeros such as 6.0 × 10⁻³ ).
B1: Correct value not in standard form (e.g. 0.006 or 0.6 × 10⁻² ), OR writing the given expression as 6 × 10⁻¹ ÷ 100 , OR correctly converting an answer with 6 as the only non-zero digit (e.g. 0.0006 = 6 × 10⁻⁴ ).
B1: Correct value not in standard form (e.g. 0.006 or 0.6 × 10⁻² ), OR writing the given expression as 6 × 10⁻¹ ÷ 100 , OR correctly converting an answer with 6 as the only non-zero digit (e.g. 0.0006 = 6 × 10⁻⁴ ).
💡 Key Knowledge
- Standard form must be written as A × 10ⁿ where 1 ≤ A < 10. Leaving the front number as 0.6 loses the final accuracy mark.
- Dividing by 100 ( 10² ) decreases the power of 10 by 2.
- Numbers smaller than 1 always have a negative power in standard form.
❌ Common Errors
- Wrong power sign: Writing 6 × 10³ instead of 6 × 10⁻³ .
- Incomplete conversion: Leaving the answer as 0.006 or 0.6 × 10⁻² (earns only 1 mark).
- Counting zeros incorrectly: Getting 0.06 (dividing by 10) or 0.0006 (dividing by 1000).
Part (b) • 2 Marks
Work out 40 × 30 × 10⁵ in Standard Form
Multiplication and converting large values
📐 Step-by-Step Calculation
- Step 1: Multiply the front numbers
40 × 30 = 1200 - Step 2: Combine with the power of 10
The expression is now 1200 × 10⁵
(As an ordinary number, this is 120 000 000 ). - Step 3: Adjust into standard form
Convert 1200 into standard form: 1.2 × 10³
Multiply powers: (1.2 × 10³) × 10⁵ = 1.2 × 10³⁺⁵ = 1.2 × 10⁸
✅ Correct Answer & Mark Scheme
1.2 × 10⁸
B2: Full marks for 1.2 × 10⁸ (condone 1.20 × 10⁸ ).
B1: Correct ordinary number 120 000 000 or "120 million", OR non-standard form values such as 12 × 10⁷ or 120 × 10⁶ , OR 1.2 × 10ᵃ × 10ᵇ where a + b = 8 , OR a value with only non-zero digits 12 correctly converted into standard form (e.g. 12 000 000 = 1.2 × 10⁷ ).
B1: Correct ordinary number 120 000 000 or "120 million", OR non-standard form values such as 12 × 10⁷ or 120 × 10⁶ , OR 1.2 × 10ᵃ × 10ᵇ where a + b = 8 , OR a value with only non-zero digits 12 correctly converted into standard form (e.g. 12 000 000 = 1.2 × 10⁷ ).
🧠 Exam Technique: Adjusting Powers
- If your front number is too large, divide it by powers of 10 until it is between 1 and 10, then add that same number of powers to the index:
1200 × 10⁵ → (1200 ÷ 1000) × (10⁵ × 10³) = 1.2 × 10⁸ - Always double-check: 120 000 000 requires the decimal point to move 8 places to the left to reach 1.2 .
❌ Common Errors
- Stopping early: Writing 1200 × 10⁵ or 12 × 10⁷ . These are numerically correct but lose the final mark because A ≥ 10 .
- Wrong power adjustment: Subtracting powers instead of adding them, giving 1.2 × 10² .
- Miscounting zeros: Miscalculating 40 × 30 as 120 instead of 1200.
Topics
Number · 3.1.1 Structure and calculation
Question and mark scheme from the AQA GCSE Mathematics examination, Paper 1 (Foundation), June 2025. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.