Measurement Examples And Worksheet - A-64 Appendix 5 Page 9
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36A-71
V.1 American Units of Measurement
Convert from one unit of time to another.
9
Self Check 9
9
EXAMPLE
Astronomy
A lunar eclipse occurs when the Earth is
A solar eclipse (eclipse
THE SUN
between the sun and the moon in such a way that Earth’s shadow darkens the
of the sun) can last as long as
moon. (See the figure below, which is not to scale.) A total lunar eclipse can last as
450 seconds. Express this time
long as 105 minutes. Express this time in hours.
in minutes.
Now Try
Problem 59
Sun
Earth
Moon
Strategy
We will multiply 105 minutes by a carefully chosen unit conversion
factor.
WHY
If 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 choose 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
1 hr
This is the unit we want to introduce.
This is the unit we want to eliminate (the original unit).
60 min
To perform the conversion, we multiply.
105 min
105 min
1 hr
Write 105 min as a fraction: 105
.
#
105 min
1
1 hr
1
60 min
Then multiply by a form of 1:
.
60 min
105 min
1 hr
Remove the common units of minutes in the numerator
#
and denominator. Notice that the units of hours remain.
1
60 min
105
hr
Multiply the fractions.
60
1
1
To simplify the fraction, prime factor 105 and 60.
3
5
7
hr
Then remove the common factors 3 and 5 in the
2 2 3
5
numerator and denominator.
1
1
7
Multiply the remaining factors in the numerator.
hr
4
Multiply the remaining factors in the denominator.
3
7
1
hr
Write as a mixed number.
4
4
3
A total lunar eclipse can last as long as
1
hours.
4
ANSWERS TO SELF CHECKS
7
1
7
3
1.
1
in. 2.
1
in. 3. 27 ft 4. 18 in. 5.
mi
0.22 mi 6.
3
lb
3.75 lb
8
4
32
4
1
7. 960 oz 8. 40 fl oz 9.
7
min
2
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