Standard Form
This topic covers 4 learning steps, guiding your child from the basics through to confident problem-solving. Each step includes a worked example and adaptive practice questions.
What Your Child Will Learn
- Write in standard form
Convert large numbers to A × 10ⁿ - Convert back
Convert standard form to ordinary number - Multiply & divide
Calculate with standard form numbers - Small numbers
Standard form for numbers less than 1
Before This Topic
Your child should be comfortable with:
- Long Multiplication (Year 4)
- Long Division (Year 5)
Common Mistakes
- Writing the number part (A) outside the valid range (e.g. writing 45 × 10³ instead of 4.5 × 10⁴)
In standard form, A must be between 1 and 10 (including 1 but not 10). So 45 × 10³ is not valid standard form — it should be 4.5 × 10⁴. Move the decimal point until you have a number between 1 and 10, then adjust the power. - Getting the power of 10 wrong for small numbers (e.g. writing 0.003 as 3 × 10³ instead of 3 × 10⁻³)
For numbers smaller than 1, the power of 10 is NEGATIVE. Count how many places you move the decimal to the right to get a number between 1 and 10. For 0.003, you move 3 places right, so it is 3 × 10⁻³.
Tips for Parents
- Explain why standard form exists: it is much easier to write 3 × 10⁸ than 300,000,000. Scientists and engineers use it for very large and very small numbers every day.
- Use real examples: the distance to the Sun is about 1.5 × 10⁸ km, a human hair is about 7 × 10⁻⁵ metres wide. Ask your child to convert these back to ordinary numbers.
- Practise the key rule: the power tells you how many places to move the decimal. Positive powers move it RIGHT (bigger numbers), negative powers move it LEFT (smaller numbers).
- When multiplying in standard form, multiply the number parts and add the powers: (2 × 10³) × (3 × 10⁴) = 6 × 10⁷. Then check the number part is still between 1 and 10.
Key Words
- Standard form — A way of writing very large or very small numbers as A × 10ⁿ, where A is between 1 and 10 — e.g. 4,500 = 4.5 × 10³.
- Power (or index) — The small raised number that shows how many times 10 is multiplied by itself — in 10⁴, the power is 4.
- Ordinary number — A number written out in full — 4,500,000 is the ordinary number for 4.5 × 10⁶.
- Negative power — A power less than zero, used for small numbers — 10⁻² = 0.01.
Where This Fits
Before this topic: Children should understand place value, be confident multiplying and dividing by 10, 100, and 1000, and know about powers of 10.
After this topic: Standard form is used extensively in science, leads to calculating with very large and small numbers, and connects to logarithms in A-level maths.
How MathCraft Teaches This
In MathCraft, Standard Form is taught through the Money, Data & Measure adventure track. Your child follows guided lessons with friendly characters, works through examples step by step, then practises with questions that adapt to their level.
The adaptive engine tracks mastery across all 4 steps, revisiting concepts your child finds tricky and advancing when they're ready. Parents can see detailed progress in the Parent Dashboard.
Practise Standard Form with MathCraft
Step-by-step lessons, worked examples, and adaptive practice — all wrapped in an adventure game your child will love.
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