Last reviewed: 7 November 2026
Updated November 2026. These Grade 9 approximations and errors notes explain how to estimate quantities, how to find the error between an estimate and the actual measurement, and how to calculate percentage error. The error is the difference between the estimated and actual values. Percentage error = (error ÷ actual value) × 100%. If you estimate a corridor is 45 m long and it measures 50 m, the error is 5 m and the percentage error is 5 ÷ 50 × 100% = 10%.
The examples and questions are original practice for Kenyan junior school learners, not an official paper. For the other Grade 9 maths topics, see our Grade 9 maths revision guide and the Grade 9 notes hub.
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What the Grade 9 Curriculum Covers
Approximations and errors is a short sub-strand under Measurements in the Kenya Institute of Curriculum Development’s Grade 9 Mathematics design. Learners approximate quantities in measurements, find errors using estimations and actual measurements, and find percentage errors. Suggested activities include estimating length, area, volume, capacity and mass, then measuring with the right instrument and comparing. The design is listed on the KICD Grade Nine curriculum designs page.
Approximating Quantities
An approximation is a sensible value close to the true one. You make approximations every day: guessing a bag of potatoes is about 2 kg, or that the walk to school is about 1 km. Good estimates use a known reference:
- A standard classroom door is roughly 2 m high, which helps estimate wall heights.
- Your stride can be measured once and used to pace out distances.
- A 500 ml bottle helps estimate the capacity of other containers.
In measurement, every reading is itself an approximation, because instruments have limited precision. OpenStax Chemistry’s section on measurement uncertainty, accuracy and precision explains why no measurement is exact.
Rounding as Approximation
Rounding is a common way to approximate. 3,486 to the nearest hundred is 3,500. 7.648 to 2 decimal places is 7.65. 0.04617 to 2 significant figures is 0.046. When estimating a calculation, round each number first: 49 × 21 ≈ 50 × 20 = 1,000 (the exact answer is 1,029).
Finding the Error
Error = estimated value − actual value (or the other way round). Many teachers quote the size of the error without a sign; a positive error then simply means “how far off”. Some ask you to say whether the estimate was too high or too low.
Worked example
A learner estimates that a jug holds 1.5 litres. Measured with a measuring cylinder, it holds 1.8 litres. Error = 1.8 − 1.5 = 0.3 litres. The estimate was 0.3 litres too low.
Percentage Error
An error of 1 cm matters a lot when measuring a pencil but hardly matters when measuring a football field. Percentage error compares the error with the size of the actual quantity:
Percentage error = (error ÷ actual value) × 100%
Worked example one
Using the jug: percentage error = 0.3 ÷ 1.8 × 100% ≈ 16.7%.
Worked example two: comparing two estimates
Achieng estimates a 200 g packet weighs 180 g. Otieno estimates a 2 kg bag of sugar weighs 1.9 kg (made-up figures).
- Achieng: error 20 g; percentage error = 20 ÷ 200 × 100% = 10%.
- Otieno: error 0.1 kg = 100 g; percentage error = 100 ÷ 2,000 × 100% = 5%.
Otieno’s error in grams was bigger, but his estimate was better as a percentage. Always convert to the same unit before dividing.
Worked example three: consumer awareness
A packet labelled 1 kg is weighed on an accurate scale and found to contain 960 g. Percentage error = 40 ÷ 1,000 × 100% = 4%. The curriculum links this kind of check to consumer awareness: knowing how to measure helps you notice short measures.
Original Practice Questions With Worked Answers
- Estimate 398 × 51 by rounding. 400 × 50 = 20,000.
- A learner estimates a room is 6 m long; it is 6.4 m. Find the error. 0.4 m.
- Find the percentage error in question 2. 0.4 ÷ 6.4 × 100% = 6.25%.
- A bucket’s capacity is estimated at 12 litres and measured as 10 litres. Find the percentage error. 2 ÷ 10 × 100% = 20%.
- Why do we divide by the actual value and not the estimate? Because the actual value is the true size we are comparing the error against.
Cover the answers and attempt each question first. For timed practice, use the Grade 9 revision papers or the Grade 9 CBC Challenge. These notes are free; full revision access is available with the KSh 20 Day Pass or the KSh 500 Monthly Pass.
Frequently Asked Questions
What is the formula for percentage error?
Percentage error = (error ÷ actual value) × 100%, where the error is the difference between the estimated and actual values.
What is the difference between an estimate and an approximation?
They are closely related. An estimate is a reasoned guess of a value; an approximation is any value close to the true one, including a rounded measurement.
Can a percentage error be more than 100%?
Yes, if the estimate is more than double the actual value. For example, estimating 25 when the actual value is 10 gives a 150% error.
Why is no measurement exact?
Every instrument has a smallest division, so readings are rounded to that division.