Standard form, significant figures and decimal places: a clear guide
How to write numbers in standard form, round to significant figures and decimal places, and avoid the classic traps with zeros — with worked examples for WAEC, NECO, JAMB and BECE.
By the Levia editorial team · Updated 27 October 2026 · 4 min read
Standard form and approximation questions are among the easiest marks on any Mathematics paper. They are also among the most commonly dropped, almost always because of zeros. This guide explains each idea clearly and shows exactly where the traps are.
Part 1: Standard form
Standard form (also called scientific notation) writes a number as:
A × 10ⁿ, where 1 ≤ A < 10 and n is a whole number (positive, negative or zero).
The number A must be at least 1 and less than 10, so 3.7 × 10⁴ is in standard form, but 37 × 10³ and 0.37 × 10⁵ are not, even though they have the same value.
Large numbers (positive powers)
Move the decimal point to the left until there is one non-zero digit before it. The number of places moved is the power.
Example: Write 48,000 in standard form.
- → 4.8000 (moved 4 places left) → 4.8 × 10⁴
Example: Write 6,250,000 in standard form.
Move 6 places → 6.25 × 10⁶
Small numbers (negative powers)
Move the decimal point to the right until there is one non-zero digit before it. The power is negative.
Example: Write 0.00074 in standard form.
0.00074 → 7.4 (moved 4 places right) → 7.4 × 10⁻⁴
Example: Write 0.0305 in standard form.
Move 2 places → 3.05 × 10⁻²
A quick check
- Numbers 10 or larger have a positive power.
- Numbers between 0 and 1 have a negative power.
- Numbers from 1 up to (but not including) 10 have power 0: 5.6 = 5.6 × 10⁰.
Calculating in standard form
Multiplying: multiply the A values, add the powers, then adjust if needed.
(3 × 10⁴) × (5 × 10³) = 15 × 10⁷ = 1.5 × 10⁸ (adjusted because 15 is not between 1 and 10).
Dividing: divide the A values, subtract the powers.
(8 × 10⁶) ÷ (2 × 10²) = 4 × 10⁴ = 4 × 10⁴.
Part 2: Decimal places
Decimal places (d.p.) count digits after the decimal point.
To round to n decimal places, look at the digit in position n + 1:
- 5 or more: round up.
- 4 or less: leave it.
Example: Round 3.14659 to 2 decimal places.
The 2nd decimal digit is 4; the next digit is 6, so round up → 3.15.
Example: Round 12.3049 to 2 decimal places.
The 2nd decimal digit is 0; the next digit is 4, so leave it → 12.30.
Notice we keep the final 0 in 12.30. It shows the answer is accurate to 2 decimal places, and leaving it off can cost a mark.
Part 3: Significant figures
Significant figures (s.f.) count digits from the first non-zero digit, whether before or after the decimal point.
The rules for zeros
This is where most errors happen:
| Type of zero | Significant? | Example |
|---|---|---|
| Leading zeros (before the first non-zero digit) | Never | 0.0045 has 2 s.f. |
| Zeros between non-zero digits | Always | 3005 has 4 s.f. |
| Trailing zeros after a decimal point | Yes | 2.50 has 3 s.f. |
| Trailing zeros in a whole number | Depends on context | 4500 has 2, 3 or 4 s.f. |
Rounding to significant figures
Find the first non-zero digit, count the required number of digits, then round using the next digit.
Example: Round 0.03456 to 2 significant figures.
First non-zero digit: 3. Two significant figures: 3 and 4. Next digit: 5, so round up → 0.035.
Example: Round 0.0048762 to 3 significant figures.
Digits: 4, 8, 7. Next digit: 6, so round up → 0.00488.
Example: Round 47,862 to 2 significant figures.
Digits: 4, 7. Next digit: 8, so round up → 48, then keep the place value with zeros → 48,000.
That last step matters: rounding 47,862 to "48" is wrong. The answer must still be roughly forty-eight thousand.
Example: Round 2.996 to 3 significant figures.
Digits: 2, 9, 9. Next digit: 6, so round up: 2.99 → 3.00. Answer: 3.00 (keep the zeros to show 3 s.f.).
Decimal places versus significant figures
Compare these for the number 0.004567:
- To 2 decimal places: 0.00 (the third decimal digit is 4, so it rounds down to 0.00)
- To 2 significant figures: 0.0046
And for 3456.78:
- To 1 decimal place: 3456.8
- To 2 significant figures: 3500
Read the question carefully. Swapping decimal places and significant figures is one of the most common mistakes in the exam.
Combining the two: standard form to s.f.
Express 0.00034521 in standard form, correct to 3 significant figures.
Round first: 0.00034521 to 3 s.f. is 0.000345 (the next digit is 2, so it rounds down).
Standard form: 3.45 × 10⁻⁴.
Common mistakes
- A not between 1 and 10 in standard form, such as 34.5 × 10⁻⁵.
- Wrong sign on the power: small numbers need negative powers.
- Counting leading zeros as significant figures.
- Dropping place-value zeros: 47,862 to 2 s.f. is 48,000, not 48.
- Dropping meaningful trailing zeros: 3.00, not 3, when 3 s.f. are required.
- Rounding in the middle of a calculation. Keep full accuracy until the final answer.
Practise for quick, accurate answers
These questions should take you under a minute each with full accuracy. Levia's Mathematics levels include standard form and approximation questions from Foundations upwards, and the junior Mathematics subject covers approximation and estimation for BECE. Every question comes with a step-by-step explanation.
Try the real Level 1 question set free — no account needed — with an explanation after every question.
Levia is an independent learning platform, not affiliated with JAMB, WAEC, NECO or any examination body. Exam formats, dates and fees can change — always confirm current details on the official body's website.