Standard Form Explained: Writing, Ordering and Calculating for GCSE Maths

The distance from the Earth to the Moon is roughly 380,000,000 metres. The width of an atom is about 0.0000000001 metres. Numbers like these are clumsy to write, easy to miscopy, and a nightmare to compare — which is exactly why GCSE Maths (and every science GCSE) uses standard form. Written that way, those two numbers become 3.8 × 10⁸ and 1 × 10⁻¹⁰: compact, readable, and easy to calculate with.

Standard form appears on both Foundation and Higher papers, calculator and non-calculator, and the marks are very winnable once you know the rules. This guide covers everything the topic can throw at you: converting in both directions, ordering, and the four operations.

What counts as standard form?

A number in standard form has exactly two parts:

A × 10ⁿ

Part	Rule	Examples that pass	Examples that fail
The front number, A	Between 1 and 10 — it can be 1, but cannot be 10	3.8, 1, 6.14, 9.04	16 (too big), 0.5 (too small)
The power, n	An integer (whole number) — negatives allowed	8, 3, −2, −10	2.6, 1.5

So 16 × 10⁴ is not standard form because 16 is greater than 10, and 3 × 10¹·⁵ fails because 1.5 isn’t an integer. But 4 × 10⁻² is perfectly fine — negative numbers are still integers.

Remember: examiners sometimes deliberately give you numbers that look like standard form but aren’t — such as 28 × 10² — especially in ordering questions. That isn’t a mistake in the paper; it’s a test of whether you’re paying attention.

Converting big numbers into standard form

Take 420,000. Two steps:

1. Build the front number. Use the significant digits to make a number between 1 and 10: here, 4.2.
2. Find the power. Imagine the decimal point sitting after the leading digit (4.2), then count how many times you multiply by 10 to get back to 420,000: 42, 420, 4,200, 42,000, 420,000 — five times. So 420,000 = 4.2 × 10⁵.

The same method handles trickier digits. For 61,400 you need all three significant digits, giving 6.14 × 10⁴. For 504,000 you must keep the zero between non-zero digits: 5.04 × 10⁵. The rule is to use every digit up to the point where only trailing zeros remain.

Tip: do not count the zeros and call that the power. It works for 7,000 = 7 × 10³ by coincidence, but 420,000 has four zeros and a power of five. Count the jumps of the decimal point instead — that method never lets you down.

Going back the other way is just repeated multiplication: 7.9 × 10⁴ means 7.9 multiplied by 10 four times — 79, 790, 7,900, 79,000.

Small numbers and negative powers

Standard form handles tiny numbers with negative powers of 10, which you can think of as repeated division by 10.

Take 0.039. The front number from the digits 3 and 9 is 3.9. Now divide 3.9 by 10 until the decimal point lands in the right place: 0.39, then 0.039 — two divisions. So 0.039 = 3.9 × 10⁻².

Reversing it works the same way: 2 × 10⁻⁴ means 2 divided by 10 four times — 0.2, 0.02, 0.002, 0.0002.

Did you know? the sign of the power tells you the size at a glance. A positive power means a big number; a negative power means a number smaller than 1. That single observation often sorts half of an ordering question before you’ve done any working.

Ordering numbers in standard form

When a question asks you to put standard-form numbers in order of size, the most reliable approach is to convert every number to an ordinary number first, order those, then write your answers in the form they were given in the question. If the paper gave you 28 × 10², your answer line should say 28 × 10² — you don’t need to correct it into standard form unless asked.

This topic pairs naturally with careful, methodical working — the same discipline covered in our guide to the non-calculator paper, where standard form questions regularly appear.

Multiplying and dividing in standard form

Here’s where the index laws earn their keep. Because everything is multiplication, you can reorder the calculation:

(3 × 10³) × (2 × 10⁵) = (3 × 2) × (10³ × 10⁵) = 6 × 10⁸

Operation	Front numbers	Powers of 10
Multiply	Multiply them	Add the powers
Divide	Divide them	Subtract the powers
Square	Multiply the number by itself	Add the power to itself

Division example: (9 × 10⁵) ÷ (3 × 10⁻²). The front numbers give 9 ÷ 3 = 3. The powers give 5 − (−2) = 5 + 2 = 7, so the answer is 3 × 10⁷. Watch that double negative — writing 10³ here (from 5 − 2) is one of the most common wrong answers in the whole topic.

When the answer isn’t in standard form

Sometimes the shortcut spits out something like (3 × 10³) × (9 × 10⁴) = 27 × 10⁷. That’s the right size but the wrong format — 27 is bigger than 10. Fix it by balancing: divide 27 by 10 to get 2.7, and compensate by multiplying 10⁷ by 10 to get 10⁸. Final answer: 2.7 × 10⁸.

It works the other way too. If a division leaves you with 0.5 × 10⁵, multiply 0.5 by 10 to get 5, and divide 10⁵ by 10 to get 10⁴, giving 5 × 10⁴. Whatever you do to one part, do the opposite to the other — the number stays the same size, only its outfit changes.

Adding and subtracting: convert first

Unlike multiplying and dividing, there’s no neat index shortcut for addition and subtraction. The recommended method is to convert to ordinary numbers, do the arithmetic, then convert back if the question wants standard form:

• 5 × 10⁴ + 2.9 × 10³ = 50,000 + 2,900 = 52,900 = 5.29 × 10⁴
• 7 × 10⁵ − 3 × 10² = 700,000 − 300 = 699,700

Always check whether the question asks for the answer in standard form or as an ordinary number — giving the right value in the wrong format throws away an easy mark.

Standard form leans heavily on the index laws, so if powers feel shaky it’s worth revisiting the fundamentals first — our post on building foundations rather than memorising explains why that pays off across every Number topic. And if you’re planning your revision timetable, slot standard form into the Number block of the 12-week GCSE Maths revision plan — it’s a classic crossover topic that appears on both tiers.

Practise standard form until it’s automatic

Standard form is a technique topic: once you’ve done enough conversions and calculations, the marks become almost free. The fastest way to get there is high-volume, focused practice.

The GCSE Number app covers the fundamentals of GCSE Maths — place value, fractions, percentages, ratio, powers, roots and rounding — which is exactly the territory standard form lives in. Drilling powers and place value there will make every conversion in this guide feel routine.

When you’re ready to mix standard form in with the rest of the syllabus, the GCSE Maths app bundles Number, Algebra, Geometry and Statistics in one place, so you can jump from a standard-form question straight into algebra or geometry practice the way real papers do. Across the four subject apps you’ll find 2900+ questions — more than enough to make sure that when 3.8 × 10⁸ turns up in your exam, it feels like an old friend.