Who this is for: Cambridge IGCSE Mathematics (0580/0607) students who want Standard Form — writing numbers as a × 10ⁿ, converting and calculating with very large and small values — to become a reliable source of marks instead of a topic they only half-remember.
What query it owns: how to understand and revise Standard Form in Cambridge IGCSE Mathematics.
Why this is safe: this page owns the Standard Form revision-guide angle, while Tutopiya’s Standard Form subtopic page owns the learning resource and the free Standard Form quiz owns the practice.

Standard Form lets you work with very large and very small numbers efficiently in Cambridge IGCSE Mathematics (0580/0607). Astronomy distances, atomic measurements and calculator displays all rely on a × 10ⁿ notation. If you can convert, calculate and compare standard-form numbers, you secure marks that many students lose on index slips. This guide explains exactly what the subtopic covers, how to handle the question types that actually appear, and where to practise each skill.

Key takeaways

• Standard form writes a number as a × 10ⁿ where 1 ≤ a < 10 and n is an integer.
• Large numbers → positive n; small numbers → negative n.
• To multiply: multiply the a values, add the indices. To divide: divide the a values, subtract indices.
• Always give the final answer in proper standard form (a must be between 1 and 10).

What is Standard Form in Cambridge IGCSE Maths?

Standard Form (also called scientific notation) is a way of writing very large or very small numbers as a × 10ⁿ, where a is at least 1 and less than 10. In Cambridge IGCSE Mathematics it covers converting to and from ordinary numbers, performing calculations, and ordering values in standard form. Examiners test both conversion and index arithmetic.

You can read the full explanation, worked examples and notes on Tutopiya’s Standard Form subtopic page before you attempt questions.

The core ideas you must master

These five ideas appear again and again. Learn what each one means and the exam phrasing that signals it.

Idea	What it means	How the exam uses it
a × 10ⁿ	a between 1 and 10, n integer	”Write 45 000 in standard form”
Positive n	Number ≥ 10 originally	3.2 × 10⁵ = 320 000
Negative n	Number < 1 originally	4.5 × 10⁻³ = 0.0045
Multiply SF	Multiply a’s, add indices	”(2 × 10³) × (3 × 10⁴)“
Divide SF	Divide a’s, subtract indices	”(8 × 10⁶) ÷ (2 × 10²)“

How to convert a number to standard form — step by step

The most reliable method is to move the decimal point and count the places.

1. Write the number with one non-zero digit before the decimal point. 45 000 → 4.5.
2. Count how many places the decimal moved — that is n. Moved 4 places right → n = 4.
3. Write as a × 10ⁿ. 45 000 = 4.5 × 10⁴.
4. For small numbers (0.00072), move right: 7.2 × 10⁻⁴ (moved 4 places, negative index).
5. After calculations, check a is still between 1 and 10; adjust if needed.

Once you have worked through a few, test yourself with the free Standard Form quiz — it tells you fast whether the method has actually stuck.

Multiply vs divide in standard form: which index rule applies?

Students lose marks by adding indices when they should subtract, or forgetting to normalise the final answer.

Operation	Rule for indices	Example
Multiply	Add indices	(2×10³)(4×10⁵) = 8×10⁸
Divide	Subtract indices	(6×10⁷)÷(2×10²) = 3×10⁵
Normalise	If a ≥ 10 or a < 1, adjust	45×10³ = 4.5×10⁴
Compare	Compare powers of 10 first	3.2×10⁶ > 5.1×10⁵

Standard Form in past-paper wording: command words that matter

Most lost marks come from misreading the command word or leaving the answer not in proper standard form.

Command word / phrase	What the question wants	Typical stem
Write … in standard form	Convert to a × 10ⁿ	”Write 0.00056 in standard form.”
Write … as an ordinary number	Expand from standard form	”Write 3.4 × 10⁻² as an ordinary number.”
Work out, giving your answer in standard form	Calculate then normalise	”Work out (4 × 10⁵) × (2 × 10³).”
Write these in order of size	Compare standard-form values	”Write 2.1×10⁴, 8×10³, 5×10⁴ in order.”
Calculate / Work out	Numerical answer, often in SF	”Calculate (9 × 10⁸) ÷ (3 × 10²).”
Give your answer correct to … s.f.	Round the coefficient a	”Give your answer correct to 2 significant figures.”

Worked exam-style stems (how to answer the wording)

Practising the wording — not just the maths — is what full marks reward.

1. “Write 0.000045 in standard form.” Move decimal 5 places right → 4.5 × 10⁻⁵. Reward: correct a, correct negative index.
2. “Work out (3 × 10⁴) × (2 × 10⁵). Give your answer in standard form.” 3 × 2 = 6; 10⁴ × 10⁵ = 10⁹ → 6 × 10⁹. Reward: indices added, answer in SF.
3. “Write 7.2 × 10⁻³ as an ordinary number.” Move decimal 3 places left → 0.0072. Reward: correct placement of zeros.

When you can recognise the wording instantly, work the full set on the Number topical past-paper questions and the Standard Form quiz to lock the method in.

How Standard Form connects to the rest of Number

Standard form builds on Estimation and Rounding Numbers for significant figures in the coefficient. Index rules extend into Exponents and Surds. When you are ready to mix topics, the Cambridge IGCSE Maths resource hub lets you move straight from a weak subtopic into the next.

Common mistakes students make

• Writing 45 × 10³ instead of normalising to 4.5 × 10⁴.
• Using a positive index for a number less than 1 (or vice versa).
• Adding indices when dividing (or subtracting when multiplying).
• Forgetting to convert the final answer back to proper standard form.

When you need more support

If standard-form conversion or calculation questions keep tripping you up, work through the Estimation and Rounding Numbers quiz and the Number topical past-paper questions to pinpoint the exact gap, then get focused help from a Cambridge IGCSE Maths tutor to fix it quickly.

Frequently asked questions

Is Standard Form hard in Cambridge IGCSE Maths? No — the rules are consistent. The challenge is normalising the final answer and applying the correct index rules when multiplying or dividing.

What is standard form? A way of writing numbers as a × 10ⁿ where 1 ≤ a < 10 and n is an integer. Example: 5 600 000 = 5.6 × 10⁶.

How do I multiply numbers in standard form? Multiply the a values together and add the powers of 10. Then check a is between 1 and 10.

How do I revise Standard Form effectively? Read the subtopic notes, practise conversions and calculations by hand, then take the Standard Form quiz to check your method.

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