phy1020.DVI

Finally, do the arithmetic:

60

mile

hr



5280 ft

1 mile



1 hr

3600 sec

D 88

ft

sec

(2.12)

Example.Convert250;000furlongs per fortnight to meters per second.
Solution.We don’t know how to convert furlongs per fortnight directly to meters per second, so we’ll have
to come up with a chain of conversion factors to do the conversion. Wedoknow how to convert: furlongs
to miles, miles to kilometers, kilometers to meters, fortnights to weeks, weeks to days, days to hours, hours
to minutes, and minutes to seconds. So we start by writing conversion factor ratios, putting units where they
need to be so that the result will have the desired target units (m/s):

250;000

furlong

fortnight



mile

furlong



km

mile



m

km



fortnight

week



week

day



day

hr



hr

min



min

sec

If you check the units here, you’ll see that almost everything cancels out; the only units left are m/s, which is
what we want to convert to. Now fill in the numbers: we want to put either the same length or the same time
in both the numerator and denominator:

250;000

furlong

fortnight



1 mile

8 furlongs



1 :609344 km

1 mile



1000 m

1km



1 fortnight

2 weeks



1 week

7 days



1 day

24 hr



1hr

60 min



1 min

60 sec

D41:58m=s

Conversions Involving Powers

Occasionally we need to do something like convert an area or volume when we know only the length conver-
sion factor.

Example.Convert 2000 cubic feet to gallons.
Solution.Let’s think about what conversion factors we know. We know the conversion factor between
gallons and cubic inches. We don’t know the conversion factor between cubic feet and cubic inches, but we
can convert between feet and inches. The conversion factors will look like this:

2000 ft^3 



in

ft

 3



gal

in^3

(2.13)

With these units, the whole expression reduces to units of gallons. Now fill in the same length in the numerator
and denominator of the first factor, and the same volume in the numerator and denominator of the second
factor:

2000 ft^3 



12 in

1 ft

 3



1 gal

231 in^3

(2.14)

Now do the arithmetic:

2000 ft^3 



12 in

1 ft

 3



1 gal

231 in^3

D14;961gallons (2.15)

2.7 Currency Units.

Money has units that can be treated like any other units, using the same techniques we’ve just seen. Two
things are unique about units of currency: