Units and rounding errors are the cheapest marks to get back, because the method is already correct. Three quick checks on every answer remove most of them.
This page belongs to SPM Mathematics. The units and significant figure checker lets you test your own values.
What are the three checks?
Run these on every numerical answer before you move on.
- Units: are all lengths in the same unit before I calculate?
- Conversion: if I converted area or volume, did I square or cube the factor?
- Rounding: did I keep full digits until the end, and round to the stated accuracy only once?
Write the target accuracy at the top of the question, so the last line of your working is already decided.
Worked example: a unit slip and a rounding slip together
An original question: a rectangular sign measures 1.8 m by 65 cm. Find its area in cm², correct to 3 significant figures, then in m².
Correct working. Convert first: 1.8 m = 180 cm. Area = 180 × 65 = 11 700 cm².
To 3 significant figures that is 11 700 cm². In m²: 11 700 ÷ 10 000 = 1.17 m².
The unit slip. A student multiplies 1.8 × 65 = 117 and writes “117 cm²”. The two lengths are in different units, so the product has no meaning.
The conversion slip. The same student then divides 117 by 100 to get m², which happens to give 1.17 here. With other numbers that shortcut fails, because 1 m² is 10 000 cm², not 100 cm².
Where does the rounding slip come from?
Rounding too early is the other pattern. Take a circle of radius 3.46 cm and find its area to 3 significant figures. If you round r² = 11.9716 to 12.0 first, then π × 12.0 = 37.7.
Keeping the full value gives π × 11.9716 = 37.6 to 3 significant figures. The early rounding changed the last digit.
Keep the calculator’s full value until the last step. Round once.
A short self-check
Try this: a path is 2.4 m long and 35 cm wide. Find its area in m², correct to 2 decimal places.
Answer
Convert 35 cm to 0.35 m. Area = 2.4 × 0.35 = 0.84 m². To 2 decimal places the answer is 0.84 m².
A student who multiplies 2.4 × 35 = 84 and writes “84” has mixed units and is wrong by a factor of 100.
Record any slip you make in the mistake log tool, tagged “unit” or “rounding”, and count each tag after a month.
When might one-to-one tuition help?
If the tags keep repeating after you have added the checks, the cause may be a habit, such as not reading the last line of the question. In a one-to-one lesson, a teacher can watch you solve and see where the unit gets dropped.
You can start with the one-hour trial class (from RM50), a real taught lesson, using your own marked papers. The fee is agreed before the trial, and the schedule is agreed with the teacher. More is on the SPM Mathematics tuition page.