IGCSE Maths 0580 · Common mistakes
Common mistakes with standard form and bounds
Updated · by the Fahmazing team
Standard form and limits of accuracy are short questions, but they are easy to get slightly wrong, and slightly wrong scores zero. Here are the slips to avoid.
1. A front number that is not between 1 and 10
In standard form the front number must be at least 1 and less than 10.
Write 45 000 in standard form
✗ Wrong: 45 × 10³ or 0.45 × 10⁵
✓ Right: 4.5 × 10⁴
Free lesson: Standard form
2. Moving the point without changing the power
If the front number gets smaller, the power must get bigger to keep the value the same.
Write 36 × 10⁵ in standard form
✗ Wrong: 3.6 × 10⁴
✓ Right: 3.6 × 10⁶, because 36 = 3.6 × 10¹, so 3.6 × 10¹ × 10⁵ = 3.6 × 10⁶
Free lesson: Standard form
3. The wrong sign on the power
A number less than 1 needs a negative power. A number of 10 or more needs a positive power.
Write 0.00062 in standard form
✗ Wrong: 6.2 × 10⁴
✓ Right: 6.2 × 10⁻⁴
Free lesson: Standard form
4. Comparing only the front numbers
Look at the power first. The bigger power is the bigger number, whatever the front numbers are.
Which is larger: 9 × 10² or 1.2 × 10⁴?
✗ Wrong: 9 × 10², because 9 is bigger than 1.2
✓ Right: 1.2 × 10⁴ = 12 000 is larger than 9 × 10² = 900
Free lesson: Standard form
5. Writing the upper bound as …4 or …49
The upper bound is the exact half-way value, even though the measurement cannot actually equal it. The lower bound is included (≤) and the upper bound is not (<).
A length is 7.3 m correct to 1 decimal place. Write down the upper bound.
✗ Wrong: 7.34 m or 7.349 m
✓ Right: 7.35 m, so 7.25 ≤ length < 7.35
Free lesson: Limits of accuracy
6. Halving the number instead of the unit
Halve the unit you rounded to, not the value itself.
A mass is 400 g to the nearest 10 g. Find the bounds.
✗ Wrong: Half of 400 is 200, so 200 ≤ m < 600
✓ Right: Half of 10 g is 5 g, so 395 ≤ m < 405
Free lesson: Limits of accuracy
7. Bounds in a calculation: bound each value first
Find the bound of each measurement, then combine them. For a division, the smallest answer comes from the smallest top divided by the largest bottom.
A runner covers 100 m (nearest metre) in 12.4 s (1 decimal place). Find the lower bound of the speed.
✗ Wrong: 99.5 ÷ 12.35 = 8.06 m/s (both lower bounds)
✓ Right: 99.5 ÷ 12.45 = 7.99 m/s (3 s.f.): smallest distance ÷ largest time
Free lessons: Limits of accuracy · Rates
Questions students ask
Why is the upper bound 7.35 and not 7.34?
Any length up to, but not including, 7.35 rounds to 7.3. The upper bound is the exact boundary value, 7.35, and the inequality uses < to show it is not included.
How do I find the maximum of a subtraction using bounds?
Use the upper bound of the first value minus the lower bound of the second. Subtracting the smallest possible amount leaves the biggest result.
Can I use my calculator for standard form?
On Paper 4, yes, but you must still write the answer correctly as a × 10ⁿ, not as the calculator display. On Paper 2 you use index laws: multiply the front numbers and add the powers.