GCSE MATHS • HIGHER TIER
Calculations with Standard Form Made Simple
Multiply and divide numbers in standard form using index laws and calculator methods.
Clear method
Exam practice
Worked proofs
Calculations with Standard Form in Four Moves
1
Separate
Separate the front numbers from the powers of ten.
2
Calculate
Multiply or divide the front numbers.
3
Use Index Laws
Add powers when multiplying and subtract powers when dividing.
4
Calculate
Make sure the final answer is written correctly in standard form.
What You’ll Learn
Recognise numbers written in standard form.
Multiply standard form numbers.
Divide standard form numbers.
Apply index laws to powers of ten.
Work confidently with negative powers.
Use a scientific calculator for standard form calculations.
Convert final answers back into correct standard form.
Key Rules
Write numbers in the form a × 10ⁿ, where 1 ≤ a < 10.
When multiplying, multiply the front numbers and add the powers.
When dividing, divide the front numbers and subtract the powers.
Keep the coefficient and power of 10 separate while calculating.
Worked Proof: Calculations with Standard Form
Step-by-Step Method
- 1. Separate
- 2. Calculate the Front Numbers
- 3. Apply the Index Law
- 4. Combine the Results
- 5. Convert if Necessary
- 6. Check the Final Answer
More Worked Examples
1
Calculate (3 × 10⁴)(2 × 10³).
Step 1 : Multiply the numbers.
3 × 2 = 6
Step 2: Add the powers.
10⁴ × 10³ = 10⁷
Step 2: Add the powers.
10⁴ × 10³ = 10⁷
2
Calculate (4 × 10⁵)(5 × 10²).
4 × 5 = 20
10⁵ × 10² = 10⁷
20 × 10⁷
Convert to standard form.
2 × 10⁸
20 × 10⁷
Convert to standard form.
2 × 10⁸
3
Calculate (8 × 10⁶) ÷ (2 × 10²).
8 ÷ 2 = 4
10⁶ ÷ 10² = 10⁴
4
Calculate (9 × 10⁵) ÷ (3 × 10²).
9 ÷ 3 = 3
10⁵ ÷ 10² = 10³
- Common GCSE Mistakes
- Forgetting to convert the final answer back into standard form.
- Adding powers when dividing.
- Subtracting powers when multiplying.
- Entering standard form incorrectly on a calculator.
- Entering standard form incorrectly on a calculator.
- Forgetting that the first number must be between 1 and 10.
- Exam Tips
- Separate the front numbers from the powers of ten.
- Add indices when multiplying powers of ten.
- Subtract indices when dividing powers of ten.
- Check negative indices carefully.
- Convert the final coefficient so that 1 ≤ a < 10.
- Use the EXP or ×10ˣ calculator key carefully.
Skills Used in Calculations with Standard Form
Standard Form
Indices
Powers of Ten
Negative Powers
Multiplication
Division
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Printable Worksheet
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Interactive Quiz
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Exam-Style Questions
Timed questions to build confidence for the real exam.
Watch the Calculations with Standard Form Tutorial
Step-by-step walkthroughs of Calculations with Standard Form with clear methods and exam tips.
Frequently Asked Questions
Standard form writes a number as a × 10ⁿ, where 1 ≤ a < 10 and n is an integer.
Add the powers of ten.
Subtract the powers of ten.
Convert the result so the first number is at least 1 but less than 10.
Yes. Negative powers are commonly used for very small numbers.
Scientific calculators commonly use an EXP or ×10ˣ key.