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

Answer:

6.82%

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:

$\%_{uncertainty} = \frac{absolute\ uncertainty}{absolute\ value}*100$

$\%_{uncertainty} = \frac{6}{88}*100$

$\%_{uncertainty} = 6.82\%$

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

$\%_{uncertainty} = \frac{absolute\ uncertainty}{absolute\ value}*100$

$\%_{uncertainty} = \frac{3}{44}*100$

$\%_{uncertainty} = 6.82\%$

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