N9NumberFoundation & Higher

Standard Form

Standard form is a tidy way of writing very large or very small numbers using powers of 10. Scientists use it constantly — and so will you for things like the speed of light or the size of an atom.

35 min Video by Maths Genie AQA GCSE Maths

Standard FormWatch the walkthrough, then read the notes below.

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What you'll learn

Write numbers in standard form
Convert between standard and ordinary form
Multiply and divide in standard form
Use the laws of indices with powers of 10

The format

A number in standard form looks like $A \times 1 0^{n}$ , where $A$ is at least 1 but less than 10, and $n$ is a whole number. A positive power means a big number; a negative power means a small one.

A \times 1 0^{n}, 1 \leq A < 10

The standard form template.

1Put the point after the first digit:

4.5

2It moved 3 places, and the number is big, so

n = 3

Answer

4.5 \times 1 0^{3}

Calculating

To multiply or divide, deal with the numbers and the powers of 10 separately, using the laws of indices. Adjust the answer so $A$ is back between 1 and 10.

Tip — On a calculator, the “×10ˣ” or “EXP” button enters standard form directly.

Remember these

A \times 1 0^{n}

Standard form, with 1 ≤ A < 10.

1 0^{m} \times 1 0^{n} = 1 0^{m + n}

Combine powers of 10.

Watch out for these

Writing

45 \times 1 0^{2}

and calling it standard form.

A must be between 1 and 10: write

4.5 \times 1 0^{3}

Using a positive power for a small number.

Small numbers (less than 1) have a negative power.

Key takeaways

Standard form: A × 10ⁿ with 1 ≤ A < 10.
Big numbers → positive n; small numbers → negative n.
Multiply/divide numbers and powers of 10 separately.

Test yourself

Ready to practise Standard Form? Pick a mode and earn XP & Dobloons.