SI - Converting Units of Time

Converting units of time is essentially identical to the process we used to convert units of distance. Since units of time are based upon multiples of 6 and 60 conversions are somewhat more involved than multiplying and dividing by ten.

Q) How many seconds are in 3.5 hours?

Remembering that:

$$1 hour = 60 minutes$$

and:

$$1 minute = 60 seconds$$

We can calculate the answer:

$$3.5 hr. \times \frac{60 min.}{hr.} \times \frac{60 sec.}{min} = 3.5 hr. \times \frac{3,600 sec.}{hr.} = 12,600 sec.$$

But how was this done?

Given that there are 60 minutes in one hour:

$$1 hour = 60 minutes$$

This can be rewritten as a ratio:

$$\frac{60 min.}{1 hr.}$$

Similarly:

$$1 minute = 60 seconds$$

Can be rewritten as:

$$\frac{60 sec.}{1 min.}$$

We can use the first ratio to convert from hours to minutes:

$$3.5 \cancel{hr.} \times \frac{60 min.}{1 \cancel{hr.}} = 210 min.$$

And use the second ratio to convert from minutes to seconds:

$$210 \cancel{min.} \times \frac{60 sec.}{1 \cancel{min.}} = 12,600 sec.$$

The above solution simply combined these steps by focusing on how to convert and cancel units:

$$3.5 \cancel{hr.} \times \frac{60 \cancel{min.}}{1 \cancel{hr.}} \times \frac{60 sec.}{1 \cancel{min.}} = 12,600 sec.$$

Since multiplication can be done in any order, you could also multiply the two ratios together to create a ratio expressing the number of seconds in an hour:

$$\frac{60 \cancel{min.}}{1 hr.} \times \frac{60 sec.}{1 \cancel{min.}} = \frac{3,600 sec.}{1 hr.}$$

And then use the new ratio to convert directly from hours to seconds:

$$3.5 \cancel{hr.} \times \frac{3,600 sec.}{1 \cancel{hr.}} = 12,600 sec.$$

Click through to the next section for a more in-depth explanation of why ratios can be used to convert between units: