Limits of Tolerance (SQA National 5 Applications of Mathematics): Revision Note

Limits of tolerance

What is tolerance?

• Tolerance is the amount that a measurement can vary from a stated value

  • e.g. a coffee machine might be stated to dispense 200 ml of hot water when a button is pressed

    • It might be acceptable for it to dispense between 199 ml and 201 ml

    • There is 1 ml tolerance

• Limits of tolerance are boundaries for acceptable measurements

  • e.g. 199 ml and 201 ml are the limits of tolerance for the coffee machine

• The limits are written using the plus or minus symbol (±)

• The limits can be given using actual amounts or percentages

  • e.g. 200 ml ± 1 ml or 200 ml ± 0.5%

How do I find the upper and lower limits?

Actual amounts

• Make sure the units are the same

  • e.g. 40 kg ± 200 g can be rewritten as 40 kg ± 0.2 kg

• Subtract the tolerance from the stated value to find the lower limit

  • e.g. 40 kg - 0.2 kg = 39.8 kg

• Add the tolerance to the stated value to find the upper limit

  • e.g. 40 kg + 0.2 kg = 40.2 kg

Percentages

• Find the percentage of the stated value to find the tolerance

  • e.g. for 25°C ± 3% find 3% of 25 to get 0.75

• Subtract the tolerance from the stated value to find the lower limit

  • e.g. 25°C - 0.75°C = 24.25°C

• Add the tolerance to the stated value to find the upper limit

  • e.g. 25°C + 0.75°C = 25.75°C

How do I use limits of tolerance?

• You might have to find the fraction or percentage of measurements that are within a tolerance of a stated amount

  • Find the limits of tolerance

  • Count the number of measurements that are within the limits of tolerance

  • Write this as a fraction or percentage of all the measurements

• You might have to determine if a measurement is within a tolerance of a stated amount

  • Find the limits of tolerance

  • Calculate the measurement or read it from a scale

  • Determine whether it is within the limits