TeXes Science Practice Test

If a thermometer shows a reading of 101.1°C in boiling water, should a student discard it based on a 0.5% error threshold?

1. No, the error is acceptable

2. Yes, the thermometer produces an error greater than 0.5%

3. Yes, it does not give a precise reading

4. No, the error is within the limit

The correct answer is: Yes, the thermometer produces an error greater than 0.5%

To determine whether the thermometer should be discarded based on a 0.5% error threshold, we first need to calculate what 0.5% of the boiling point of water, which is 100°C, would be. 0.5% of 100°C is calculated as follows: \[ 0.5/100 \times 100 = 0.5°C \] This means that the thermometer's reading needs to be within 0.5°C of the true temperature of 100°C to be considered accurate. The acceptable range of readings for accuracy would therefore be: \[ 100°C - 0.5°C = 99.5°C \] \[ 100°C + 0.5°C = 100.5°C \] So, any reading between 99.5°C and 100.5°C would be deemed acceptable. The thermometer, however, shows a reading of 101.1°C. To determine if this falls outside the acceptable range, we can observe that: \[ 101.1°C - 100°C = 1.1°C \] This indicates that the thermometer's reading exceeds the true boiling point of water by 1.1°C,