Standard form

🔗What you need to know first

How to

Standard form (scientific notation) is a way of writing very large or very small numbers concisely.

$$a \times 10^n \quad \text{where } 1 \leq a < 10 \text{ and } n \text{ is an integer}$$

Large numbers: $3,400,000 = 3.4 \times 10^6$ Small numbers: $0.000052 = 5.2 \times 10^{-5}$

Multiplying in standard form: $$(3 \times 10^4) \times (2 \times 10^3) = 6 \times 10^7$$

Adding/subtracting: convert to the same power of 10 first, or convert back to ordinary numbers.

$$(3.5 \times 10^5) + (2 \times 10^4) = 35 \times 10^4 + 2 \times 10^4 = 37 \times 10^4 = 3.7 \times 10^5$$

The result must always be back in standard form ($1 \leq a < 10$).

Common error: writing $13.4 \times 10^5$ — the digit part must be between 1 and 10. Adjust: $13.4 \times 10^5 = 1.34 \times 10^6$.

Common topics that go alongside

❓Questions to practise

New to Bow Tie Maths? It generates questions on this topic, marks them instantly, and tracks what you've mastered. Free to sign up.

📝Past paper questions

💬What the examiners say

"A significant number of candidates scored only 1 mark out of the 2 marks available because they could work out the value of the numerical expression as an ordinary number but either did not attempt to put it in standard form or could not write it correctly in standard form. A significant number of candidates lost marks because they rounded prematurely."

⬆️How you can quickly improve

When entering standard form into a calculator, put each number in brackets so the calculator treats it as a single value.
Write the index law explicitly: when multiplying powers of 10, you add the indices — 10ᵃ × 10ᵇ = 10^(a+b).
After multiplying, check that the first part of your answer is between 1 and 10 — if not, move the decimal point and adjust the power accordingly.

💡Watch

ℹ️Calculator tricks

Use the $\times 10^x$ key to enter standard form directly. The ENG button converts to engineering notation.