GCSE
Standard Form
This one is actually easier than it looks. If you can count how many places a decimal point moves, you can do standard form.
What Your Child Is Learning
Standard form is a way of writing very large or very small numbers compactly. Instead of writing out all the zeros, you express the number as something between 1 and 10 multiplied by a power of 10.
$$3{,}400{,}000 = 3.4 \times 10^6$$
$$0.00045 = 4.5 \times 10^{-4}$$
The key rule is that the first number must be between 1 and 10 (including 1, but not 10). So \(3.4\) is fine, but \(34\) or \(0.34\) would not be standard form.
Scientists use this all the time — the distance to the Sun is about \(1.5 \times 10^{8}\) km, which is much easier to work with than 150,000,000 km.
How Schools Teach It Now
The method is based on counting how many places the decimal point moves:
For large numbers:
- Place the decimal point after the first non-zero digit (e.g. \(3{,}400{,}000\) becomes \(3.4\)).
- Count how many places you moved it to the left. That number becomes the positive power of 10.
- \(3{,}400{,}000 = 3.4 \times 10^6\) (moved 6 places left).
For small numbers:
- Place the decimal point after the first non-zero digit (e.g. \(0.00045\) becomes \(4.5\)).
- Count how many places you moved it to the right. That number becomes the negative power of 10.
- \(0.00045 = 4.5 \times 10^{-4}\) (moved 4 places right).
Here are a few examples:
| Ordinary Number | Standard Form | Power |
|---|
| 56,000 | \(5.6 \times 10^4\) | +4 |
| 7,200,000 | \(7.2 \times 10^6\) | +6 |
| 0.003 | \(3 \times 10^{-3}\) | -3 |
| 0.0000081 | \(8.1 \times 10^{-6}\) | -6 |
Parent tip
A handy way to remember: big numbers get positive powers, tiny numbers get negative powers — \(10^6\) means a million, \(10^{-4}\) means a ten-thousandth.
Common Mistakes to Watch For
Classic mistake
The first number is not between 1 and 10. Writing \(34 \times 10^5\) instead of \(3.4 \times 10^6\) is NOT standard form, even though the value is the same. The first number must always be at least 1 and less than 10. This usually loses marks.
Watch out
Wrong sign on the power for small numbers. Students sometimes write \(4.5 \times 10^{4}\) when they mean \(4.5 \times 10^{-4}\). The negative sign is crucial — it is the difference between 45,000 and 0.00045.
Calculation errors
Multiplying and dividing in standard form. When the question asks students to calculate with standard form numbers, they sometimes muddle the powers. The rule is: when multiplying, add the powers. When dividing, subtract them. And always check the result is still in standard form.
$$(3 \times 10^4) \times (2 \times 10^3) = 6 \times 10^7$$
Try It Together
Here is one to work through:
Write 0.00045 in standard form.
- Find the first non-zero digit: it is 4.
- Place the decimal point after it: \(4.5\) (we keep the 5 because it is the next significant digit).
- Count how many places the decimal point moved to the right: from \(0.0004\underline{5}\) to \(4.5\) is 4 places.
- Since the original number is small (less than 1), the power is negative.
- Answer: \(4.5 \times 10^{-4}\).
$$0.00045 = 4.5 \times 10^{-4}$$
You can check: \(4.5 \times 10^{-4}\) means \(4.5 \div 10{,}000 = 0.00045\). It matches.
Conversation starter
Ask your child: "The Earth weighs about 5,970,000,000,000,000,000,000,000 kg. How would you write that in standard form?" (Answer: \(5.97 \times 10^{24}\) kg.) It is a great example of why standard form exists — nobody wants to count those zeros.
Let Them Practise
Standard form is one of those topics that clicks quickly with a bit of practice. Once your child is confident with the decimal-point-counting method, they can convert numbers in seconds.
We have a free game that turns standard form practice into a fast-paced challenge:
MaffsGames needs no account and no sign-up; what it records while your child plays is set out on the privacy page.