Secondary 3 G2 Mathematics Tutor Bukit Timah | Percentage Error, Bounds and Estimation. Did you know? A small absolute error can be a large percentage error when the reference value is small.
This Secondary 3 G2 Mathematics tutor guide for Bukit Timah families explains percentage error, bounds and estimation with worked examples, checks and realistic limits. Read the quick answer first, then use the relevant section to repair a specific misunderstanding.
Quick answer
If an estimated length is 9.8 cm and the accepted reference is 10.0 cm, absolute error is |9.8−10.0|=0.2 cm. Percentage error relative to the reference is 0.2/10.0×100%=2%. Always identify the reference denominator.
Find the exact question
Absolute error · Percentage error · Same error, different percentage · Rounding to the nearest centimetre · Bounds on a sum · Estimate before calculating · Significant figures · Rounding can compound · Difference between accuracy and precision · Scope note
Absolute error
If an estimated length is 9.8 cm and the accepted reference is 10.0 cm, absolute error is |9.8−10.0|=0.2 cm.
Try a new example with changed values and explain why the method applies. Check the original conditions and units rather than relying only on a calculator result.
Percentage error
Percentage error relative to the reference is 0.2/10.0×100%=2%. Always identify the reference denominator.
Try a new example with changed values and explain why the method applies. Check the original conditions and units rather than relying only on a calculator result.
Same error, different percentage
An absolute error of 0.2 cm against 2.0 cm is 10%, while against 20.0 cm it is 1%. The error’s significance depends on the scale.
Try a new example with changed values and explain why the method applies. Check the original conditions and units rather than relying only on a calculator result.
Rounding to the nearest centimetre
A recorded length of 12 cm to the nearest centimetre represents a true length from 11.5 cm inclusive up to but not including 12.5 cm, under ordinary half-up rounding for positive values.
Try a new example with changed values and explain why the method applies. Check the original conditions and units rather than relying only on a calculator result.
Bounds on a sum
If two positive lengths are each rounded to the nearest centimetre as 12 cm and 8 cm, their sum is at least 11.5+7.5=19 cm and less than 12.5+8.5=21 cm.
Try a new example with changed values and explain why the method applies. Check the original conditions and units rather than relying only on a calculator result.
Estimate before calculating
A bill of $19.80, $30.20 and $49.90 is close to $20+$30+$50=$100. Exact total is $99.90. The estimate is a quick magnitude check.
Try a new example with changed values and explain why the method applies. Check the original conditions and units rather than relying only on a calculator result.
Significant figures
0.004786 to three significant figures is 0.00479. Leading zeros do not count as significant digits.
Try a new example with changed values and explain why the method applies. Check the original conditions and units rather than relying only on a calculator result.
Rounding can compound
If an intermediate result is 2.746, rounding immediately to 2.7 can change later multiplication. Keep sufficient working precision and round at the end as instructed.
Try a new example with changed values and explain why the method applies. Check the original conditions and units rather than relying only on a calculator result.
Difference between accuracy and precision
A reading may be precise in displayed decimal places yet inaccurate against a reference. More digits alone do not guarantee a correct measurement.
Try a new example with changed values and explain why the method applies. Check the original conditions and units rather than relying only on a calculator result.
Scope note
Bounds and percentage error are useful mathematical extensions for interpreting measurements. Check the exact K210 syllabus and school chapter before treating every advanced bounds problem as examinable.
Try a new example with changed values and explain why the method applies. Check the original conditions and units rather than relying only on a calculator result.
A seven-day revision routine
Day 1: identify the key definition and the given quantities. Day 2: reproduce a worked example with reasons. Day 3: change the numbers. Day 4: solve an unlabelled problem. Day 5: diagnose the first error. Day 6: combine the idea with another topic. Day 7: retest independently after a delay.
Frequently asked questions
How should I start? Name the unknown and what the question actually asks. How can I verify the answer? Substitute it into the original information and check that all restrictions are met. Why can a correct-looking number be wrong? The model may have used the wrong reference, denominator or condition.
Official syllabus and tutorial context
Consult the 2027 SEC G2 Mathematics K210 syllabus for the exact assessment scope. The unchanged eduKateSG three-pupil Mathematics reference describes tutorials near Sixth Avenue. Confirm the current tutor, class fit, fees, venue and timetable directly.
Further Mathematics revision
Related resources: Quadratic Graphs, Standard Form and Accuracy and Probability Rules.