5.3 American Units of Measurement 451

EXAMPLE (^9) Astronomy A lunar eclipse occurs when the Earth is
between the sun and the moon in such a way that Earth’s shadow darkens the
moon. (See the figure below, which is not to scale.) A total lunar eclipse can last as
long as 105 minutes. Express this time in hours.
StrategyWe will multiply 105 minutes by a carefully chosen unit conversion
factor.
WHYIf we multiply by the proper unit conversion factor, we can eliminate the
unwanted units of minutes and convert to hours.
Solution
To convert from minutes to hours, we must chose a unit conversion factor whose
numerator contains the units we want to introduce (hours), and whose
denominator contains the units we want to eliminate (minutes). Since there is
1 hour for every 60 minutes, we will use
To perform the conversion, we multiply.
Write 105 min as a fraction: 105.
Then multiply by a form of 1:.
Multiply the fractions.
Write as a mixed number.
A total lunar eclipse can last as long as 1 34 hours.
7
 (^1 4)
3
4 hr
Multiply the remaining factors in the numerator.
 (^) Multiply the remaining factors in the denominator.

7

4

hr

To simplify the fraction, prime factor 105 and 60.

Then remove the common factors 3 and 5 in the

numerator and denominator.



3

1

 5

1

 7

2  2  3

1

 5

1

hr



105

60

hr

Remove the common units of minutes in the numerator

 (^) and denominator. Notice that the units of hours remain.
105 min
1

1 hr

60 min
1 hr
60 min^
105 min
105 min105 min^1
1

1 hr

60 min
This is the unit we want to introduce.
 This is the unit we want to eliminate (the original unit).
1 hr 
60 min
Sun Earth Moon
Self Check 9
THE SUNA solar eclipse (eclipse
of the sun) can last as long as
450 seconds. Express this time
in minutes.
Now TryProblem 59

1. in. 2. in. 3.27 ft 4.18 in. 5. mi 0.22 mi 6. lb3.75 lb
   7.960 oz 8.40 fl oz 9. 7 12 min

1 87 1 14 327 3 43

ANSWERS TO SELF CHECKS

9 Convert from one unit of time to another.