Key ideas
What tolerance means
Nothing is made exactly the right size. A tolerance says how far from the target size is still acceptable.
25 ± 0.3 mm
Target 25 mm, allowed to be 0.3 mm over or under.
Limits
Lower limit = target − tolerance
Upper limit = target + tolerance
25 ± 0.3: from 24.7 mm to 25.3 mm
From limits back to tolerance
Target = upper + lower2
Tolerance = upper − lower2
Acceptable?
A measurement is acceptable if it is between the limits (or exactly on one).
Always quote the limits when you explain.
Calculating limits
A bolt is made to a length of 40 ± 0.5 mm. Find the lower and upper limits.(2 marks)
Lower limit: take away.40 − 0.5 = 39.5 mm✓1
In plain EnglishThe bolt can be up to 0.5 mm shorter than 40 mm.
Upper limit: add.40 + 0.5 = 40.5 mm✓2
In plain EnglishThe bolt can be up to 0.5 mm longer than 40 mm.
From limits to tolerance
The weight of a bag of flour must be between 1.46 kg and 1.54 kg. Write this in the form target ± tolerance.(2 marks)
Find the target: halfway.Target = 1.54 + 1.462 = 32 = 1.5 kg✓1
In plain EnglishThe target is exactly halfway between the limits: add them and halve.
Find the tolerance.Tolerance = 1.54 − 1.462 = 0.082 = 0.04 kg1.5 ± 0.04 kg✓2
In plain EnglishThe gap between the limits is 0.08 kg. Half of that is above the target and half is below, so the tolerance is 0.04 kg.
Is it acceptable?
A pipe should be 120 ± 2 mm long. A pipe measures 117.5 mm. Is it acceptable? Give a reason.(2 marks)
Find the limits.120 − 2 = 118 mm120 + 2 = 122 mm✓1
In plain EnglishWork out the smallest and largest lengths allowed.
Compare and explain.117.5 mm < 118 mm, so it is not acceptable✓2
In plain EnglishQuote the numbers: 117.5 is below the lower limit of 118, so the pipe is too short.
⚠ Marks are lost for just "no". Give the limits and compare them with the measurement.
Tolerance in context
Chocolate bars should weigh 45 ± 1.5 g. Five bars weigh: 44.2 g, 46.8 g, 43.4 g, 45.9 g, 46.5 g. How many bars are acceptable?(2 marks)
Find the limits.45 − 1.5 = 43.5 g45 + 1.5 = 46.5 g✓1
In plain English± 1.5 means the weight can be up to 1.5 g less or 1.5 g more than 45 g. Take away 1.5 for the lowest weight and add 1.5 for the highest.
Check each bar.44.2 ✓, 46.8 ✗ (too heavy), 43.4 ✗ (too light), 45.9 ✓, 46.5 ✓ (on the limit)3 bars are acceptable✓2
In plain EnglishA bar that is exactly on a limit is still acceptable.
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Your turn
Calculator allowed. When you decide if something is acceptable, check it against both limits. Stuck? Tap Need a hint?