Practice · Grade 7 percentages
Percent Error — Practice
Drills in rising difficulty for percent error, plus one boss question. Each task comes with a hint and full working. Grade 7, free.
Q1 of 6
0 correct
Find the percent error:
measured 110, true 100
Quick answer
What is the best way to practise percent error?
Work through several tasks in rising difficulty. Always apply the same formula: |measured − true| ÷ |true| · 100. Remember to take the absolute value — the error is always positive — and divide by the true value, not the measured value. Practise tasks with awkward, very small results such as 0.1019% too, and run a quick sanity check after each one: if the values are close together, the error must be small.
HowTo
A 4-step solving strategy
This order works for every percent-error task — whether the reading is too high or too low.
- 1Step 1 of 4
Mark the measured and the true value
Read off which value was measured and which is the accepted (true) value. In "measured 48, true 50", 48 is the measurement and 50 is the true value. The true value is the reference.
- 2Step 2 of 4
Take the absolute deviation: |measured − true|
Subtract the values and take the absolute value so the error is positive. |48 − 50| = 2. The sign does not matter.
- 3Step 3 of 4
Divide by the true value, then times 100
Divide the deviation by the absolute true value and multiply by 100: 2 ÷ 50 · 100 = 4%. For awkward values, just carry out the division, e.g. 0.01 ÷ 9.81 · 100 ≈ 0.1019%.
- 4Step 4 of 4
Sanity-check the result
Check: if the measured and true values are close, the error must be small. A large percent error for nearly equal values points to a slip in the arithmetic.
Examples
Worked practice problems with full working
Four typical tasks from physics and maths lessons. Try each one yourself first, then compare with the working.
Easy
measured 102, true 100
|102 − 100| ÷ 100 · 100
= 2 ÷ 100 · 100
= 2%
Sanity check: values close together → small error ✓
A classic case. Deviation 2, the reference is the true value 100.
Medium
measured 47, true 50
|47 − 50| ÷ 50 · 100
= 3 ÷ 50 · 100
= 6%
Sanity check: reads low → error still positive ✓
The measurement is smaller than the true value, but the absolute value keeps the error positive.
Medium
measured 7, true 8
|7 − 8| ÷ 8 · 100
= 1 ÷ 8 · 100
= 12.5%
Sanity check: 1 ÷ 8 = 0.125 → 12.5% ✓
An awkward result. Don't fear decimals: 1 divided by 8 is 0.125.
Hard
measured 3.14, true 3.14159
|3.14 − 3.14159| ÷ 3.14159 · 100
= 0.00159 ÷ 3.14159 · 100
≈ 0.0506%
Sanity check: tiny difference → very small error ✓
Approximating π with 3.14 is off by only about five hundredths of a percent.
Pitfalls
Common mistakes — and how to avoid them
These five traps show up again and again with percent error.
Dividing by the measured value
The error is relative to the true value. Divide by true, not by measured. With measured 48 and true 50 it is 4%, not 4.17%.
Forgetting the absolute value
Percent error is always positive. Even when the reading is too low, no minus sign belongs on the result — the absolute value in the numerator takes care of that.
Confusing it with percent change
Percent change can carry a sign and is relative to the old value. Percent error is always positive and relative to the true value.
Treating awkward, tiny results as wrong
Not every percent error is round. 9.8 vs 9.81 gives ≈ 0.1019% — that is perfectly correct. Just carry out the division precisely.
Forgetting the times 100
0.01 ÷ 9.81 gives 0.00102 — that is not yet a percentage. Only multiplying by 100 turns it into ≈ 0.1019%.
Study
Practise with a plan — three quick tips
15 minutes at a time, not 90 in one go
Three short practice sessions over three days stick better than one long session the night before the test. The keyword is "spaced repetition".
Solve first, then look at the answer
Write down your working before you reveal the hint. Active recall is three to four times more effective for learning than passive reading.
On every wrong answer: ask why
Was it the wrong reference value? A missing absolute value? Note the cause — next time you will spot the mistake straight away.
FAQ
Frequently asked practice questions
Glossary
Terms in one sentence
- Percent error
- The relative deviation in percent: |measured − true| ÷ |true| · 100.
- Measured value
- The measured or estimated value being checked.
- True value
- The accepted, theoretical value — it sits in the denominator and is the reference.
- Absolute deviation
- The magnitude of the difference between measured and true value, in the unit of the quantity.
- Absolute value
- The value without its sign — it keeps the error positive.
- Relative
- Expressed against a reference, here the true value; dimensionless.
- Accuracy
- A small percent error means high accuracy of the measurement.