Tolerance is the amount by which a measurement is allowed to vary from a stated value and still be acceptable. A coffee machine set to pour 200 ml with a tolerance of 1 ml is working properly anywhere between 199 ml and 201 ml.

What are the limits of tolerance, and how do you find them?

They are the largest and smallest acceptable measurements. Subtract the tolerance from the stated value for the lower limit, and add it for the upper limit, which is what the plus or minus symbol is telling you to do.

A tolerance is given as 40 kg ± 200 g. What must you do before finding the limits?

Put both quantities into the same unit. 200 g is 0.2 kg, so the tolerance can be rewritten as 40 kg ± 0.2 kg. The limits are then 39.8 kg and 40.2 kg; subtracting 200 from 40 directly would be nonsense.

True or False? A rod measuring exactly 35.3 mm is within a tolerance of 35 mm ± 0.3 mm.

True. The limits themselves count as acceptable, so a measurement landing exactly on the upper or lower limit is within tolerance. It is worth checking the boundary values deliberately, because they are easy to skip over when scanning a list.

True or False? To count the divisions between two labelled values, you count the marks between them.

False. A division is a gap , not a mark, so you count the spaces rather than the lines. Between 20 and 30 there may be only four marks in between, but there are five gaps, and using four would make every reading wrong.

Once you know what a division is worth, how do you read a value off a scale?

Check which way round the numbers are increasing first. Then count the divisions on from the last labelled value, and add on that many division-values. So on a scale of 2 units per division, two divisions past 60 reads as 64.

What does it mean if a scale has major, sub and minor divisions?

The scale is marked at three different levels of fineness at once. The major divisions might go up in 20s, the subdivisions in 5s and the minor divisions in 1s, so you have to be clear which size of gap you are counting in before reading anything off.

A pressure gauge is marked in both kPa and psi. How do you use it?

Treat the two scales completely separately, working out the value of one division on each. Once both are understood, the instrument can be used either to convert a reading from one unit into the other, or to compare two measurements that were given in different units.

Monday's temperature was 18.5°C and Tuesday's was 64°F. How can a thermometer marked in both units settle which was warmer?

Monday was warmer. Work out each scale's division value, then mark both temperatures on the thermometer: 18.5°C sits three and a half divisions above 15°C, and 64°F sits two divisions above 60°F. Whichever mark is higher up the thermometer is the warmer day, and here that is Monday's.

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Tolerance & Reading Scales (SQA National 5 Applications of Mathematics): Flashcards

Exam code: X844 75

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FrontLimits of Tolerance
Define tolerance.

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Define tolerance.
Tolerance is the amount by which a measurement is allowed to vary from a stated value and still be acceptable.
A coffee machine set to pour 200 ml with a tolerance of 1 ml is working properly anywhere between 199 ml and 201 ml.
What are the limits of tolerance, and how do you find them?
They are the largest and smallest acceptable measurements.
Subtract the tolerance from the stated value for the lower limit, and add it for the upper limit, which is what the plus or minus symbol is telling you to do.
How do you find the limits when the tolerance is a percentage, as in 25°C ± 3%?
Work out the percentage of the stated value first, to turn it into an actual amount.
3% of 25 is 0.75, so the tolerance is 0.75°C.
The limits are then $25 - 0.75 = 24.25$ °C and $25 + 0.75 = 25.75$ °C.
A tolerance is given as 40 kg ± 200 g. What must you do before finding the limits?
Put both quantities into the same unit.
200 g is 0.2 kg, so the tolerance can be rewritten as 40 kg ± 0.2 kg.
The limits are then 39.8 kg and 40.2 kg; subtracting 200 from 40 directly would be nonsense.
Rods must be 35 mm ± 0.3 mm. Complete the limits:
$lower = 35 - 0.3 =______mm and upper = 35 + 0.3 =______mm$
The completed limits are:
$lower = 35 - 0.3 = 34.7 mm and upper = 35 + 0.3 = 35.3 mm$
Any rod measuring between these two figures is acceptable.
True or False?
A rod measuring exactly 35.3 mm is within a tolerance of 35 mm ± 0.3 mm.
True.
The limits themselves count as acceptable, so a measurement landing exactly on the upper or lower limit is within tolerance.
It is worth checking the boundary values deliberately, because they are easy to skip over when scanning a list.
How do you find the fraction of a sample that is within tolerance?
Work out the two limits first, then go through the measurements counting how many fall between them.
Write that count over the total number in the sample, and simplify: 12 rods out of 15 gives $\frac{12}{15}$ , which is $\frac{4}{5}$ .
Complete the method for a marked scale on an instrument:
To find what one small division is worth, take the $______$ between two labelled values and $______$ it by the number of divisions between them.
The completed method is:
To find what one small division is worth, take the difference between two labelled values and divide it by the number of divisions between them.
Any pair of labelled values will do, so pick whichever pair is easiest to work with.
A thermometer is labelled 20°C and 30°C with 5 divisions between them. What is each division worth?
Each division is worth 2°C.
The difference between the labelled values is 10°C, and $10 \div 5 = 2$ .
True or False?
To count the divisions between two labelled values, you count the marks between them.
False.
A division is a gap, not a mark, so you count the spaces rather than the lines.
Between 20 and 30 there may be only four marks in between, but there are five gaps, and using four would make every reading wrong.
Once you know what a division is worth, how do you read a value off a scale?
Check which way round the numbers are increasing first.
Then count the divisions on from the last labelled value, and add on that many division-values.
So on a scale of 2 units per division, two divisions past 60 reads as 64.
What does it mean if a scale has major, sub and minor divisions?
The scale is marked at three different levels of fineness at once.
The major divisions might go up in 20s, the subdivisions in 5s and the minor divisions in 1s, so you have to be clear which size of gap you are counting in before reading anything off.
A pressure gauge is marked in both kPa and psi. How do you use it?
Treat the two scales completely separately, working out the value of one division on each.
Once both are understood, the instrument can be used either to convert a reading from one unit into the other, or to compare two measurements that were given in different units.
Monday's temperature was 18.5°C and Tuesday's was 64°F. How can a thermometer marked in both units settle which was warmer?
Monday was warmer.
Work out each scale's division value, then mark both temperatures on the thermometer: 18.5°C sits three and a half divisions above 15°C, and 64°F sits two divisions above 60°F.
Whichever mark is higher up the thermometer is the warmer day, and here that is Monday's.

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