Math 30-3 Precision, Accuracy and Tolerance

A machine part has a nominal dimension of 50.00 mm with a tolerance of ±0.05 mm. What is the maximum allowable dimension?

• 49.95 mm

• 50.00mm

• 50.05mm

• 50.10mm

Answer explanation

The nominal dimension is 50.00 mm with a tolerance of ±0.05 mm. To find the maximum allowable dimension, add the tolerance to the nominal dimension: 50.00 mm + 0.05 mm = 50.05 mm. Thus, the correct answer is 50.05 mm.

In a manufacturing process, the acceptable weight range for a product is 100.00 g ± 0.10 g. What is the minimum acceptable weight?

• 99.80 g

• 99.90g

• 100.00g

• 100.10g

Answer explanation

The acceptable weight range is 100.00 g ± 0.10 g, meaning the minimum acceptable weight is 100.00 g - 0.10 g = 99.90 g. Therefore, the correct answer is 99.90 g.

A shaft diameter is specified as 25.00 mm ± 0.03 mm. Which of the following measurements falls within the acceptable range?

• 24.96 mm

• 24.98mm

• 25.04mm

• 25.05mm

Answer explanation

The specified range is 24.97 mm to 25.03 mm. Among the options, 25.04 mm is the only measurement that falls within the acceptable range, as it is just above the upper limit of 25.03 mm.

The tolerance for a bolt length is given as 75.00 mm ± 0.08 mm. What is the total tolerance range?

• 0.08 mm

• 0.16mm

• 0.24mm

• 0.32mm

Answer explanation

The total tolerance range is calculated by adding the positive and negative tolerances: 0.08 mm + 0.08 mm = 0.16 mm. Therefore, the correct answer is 0.16 mm.

A circuit board component has a resistance of 100.00 Ω with a tolerance of ±2%. What is the maximum allowable resistance?

• 98.00 Ω

• 100.00Ω

• 102.00Ω

• 104.00Ω

Answer explanation

To find the maximum allowable resistance, calculate 2% of 100.00 Ω, which is 2.00 Ω. Adding this to the nominal value gives 100.00 Ω + 2.00 Ω = 102.00 Ω. Thus, the maximum allowable resistance is 102.00 Ω.

The thickness of a metal sheet is specified as 1.50 mm ± 0.02 mm. Is a measurement of 1.53 mm within the tolerance?

• yes, its within the upper limit

• no, it exceeds the upper limit

• yes, it's exactly at the upper limit

• no, it's below the lower limit

Answer explanation

The specified thickness is 1.50 mm ± 0.02 mm, meaning the upper limit is 1.52 mm. A measurement of 1.53 mm exceeds this limit, so the correct answer is 'no, it exceeds the upper limit'.

A chemical solution requires a pH of 7.00 ± 0.05. Which of the following pH values is outside the acceptable range?

• 6.96

• 6.98

• 7.04

• 7.06

Answer explanation

The acceptable pH range is 6.95 to 7.05. The value 7.06 exceeds this range, making it the only option outside the acceptable limits.

The nominal dimension of a part is 30.00 mm with a tolerance of ±0.03 mm. What is the lower limit of the acceptable range?

• 29.96mm

• 29.97mm

• 30.00mm

• 30.03mm

Answer explanation

The nominal dimension is 30.00 mm with a tolerance of ±0.03 mm. To find the lower limit, subtract the tolerance from the nominal dimension: 30.00 mm - 0.03 mm = 29.97 mm. Thus, the lower limit is 29.97 mm.

The allowable temperature range for a process is 150.00°C ± 1.50°C. Is a temperature of 151.60°C within the specified tolerance?

• yes, it's withing the upper limit

• no, it exceeds the upper limit

• yes, it's exactly at the upper limit

• no, it's below the lower limit.

Answer explanation

The allowable range is 150.00°C ± 1.50°C, which means the upper limit is 151.50°C. A temperature of 151.60°C exceeds this limit, so the correct answer is 'no, it exceeds the upper limit'.

Which of the following instruments would likely provide the most precise measurement of a person's height?

• a standard tape measure

• a laser rangefinder

• a ruler

• a smartphone app using the device's camera

Answer explanation

A laser rangefinder uses laser technology to measure distances accurately, making it the most precise option for measuring height compared to a tape measure, ruler, or smartphone app.