Question

If 44 ± 3 beats are counted (in exactly 30 s) what is the percent uncertainty in the measurement of their heartbeats per minute?

Answer 1

The heart rate is 88 ± 6 beats per minute, and the percent uncertainty in this measurement is 6.8%.

Step-by-step explanation:

To calculate the percent uncertainty in the measurement of heartbeats per minute, we need to determine the range of possible values for the heart rate. In this case, the student counted 44 ± 3 beats in 30 seconds. To find the heart rate in beats per minute, we can multiply the number of beats by 2 since there are 60 seconds in a minute. Therefore, the heart rate is (44 ± 3) * 2 = 88 ± 6 beats per minute.

The percent uncertainty in this measurement can be calculated by dividing the uncertainty by the measured value and multiplying by 100. So, the percent uncertainty is (6 / 88) * 100 = 6.8%.

Answer 2

6.82%

Step-by-step explanation:

If 44 ±3 beats are counted in 30 seconds, twice the number of beats will be counted in 1 minute or 60 seconds, i.e. 88 beats per minute. The absolute uncertainty in 1 minute will also be twice the uncertainty in 30 seconds, so 88 ±6 beats per minute.

The percentage uncertainty can be found by below:

`\%_(uncertainty) = (absolute\ uncertainty)/(absolute\ value)*100`

`\%_(uncertainty) = (6)/(88)*100`

`\%_(uncertainty) = 6.82\%`

The percentage uncertainty can also be found for the 30 second interval

`\%_(uncertainty) = (absolute\ uncertainty)/(absolute\ value)*100`

`\%_(uncertainty) = (3)/(44)*100`

`\%_(uncertainty) = 6.82\%`

While the absolute uncertainty varies depending on the time interval, the percentage uncertainty remains the same: 6.82%