# Question #06e24

Sep 8, 2017

19800 seconds

#### Explanation:

We can use conversion factors to find out how many seconds are in 5 hours and 30 minutes. We could either split this up and first find out how many seconds are in 5 hours and then find how many seconds are in 30 minutes, or we can say that 5 hours and 30 minutes = 5.5 hours (5 and a half hours) and do one calculation.

We will use the following conversion factor ratios throughout the calculation:

$\frac{1 h o u r}{60 \min}$ and $\frac{1 \min}{60 \sec}$

Those conversation factors just mean that 1 hour=60 minutes and 1 minute=60 seconds. We could write them the other way around, too (as reciprocals).

To calculate how many seconds are in 5.5 hours:

$5.5 h r s$ X $\frac{60 \min}{1 h o u r}$ X $\frac{60 \sec}{1 \min}$ =
$5.5 h r s$ X $60 \sec$ = $19800 \sec$

We end up with the final unit as seconds since, with ratios, if you have the top unit the same as the bottom unit, then the units cancel out - so the unit of hours in the numerator of our calculation cancels out with the unit of hours in the denominator of our calculation, and the same goes for the minutes, so we end up with just seconds.