Hfcc Math Lab Nat 05 Conversions Using Dimensional Analysis Worksheet With Answer Key - 2011 Page 3
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5Ex 2: How many miles are in 400 km?
(
)
=
×
400 km
400 km 1
Multiplying by 1 does not change the value of 400 km.
0.621 mi
=
=
Since 1 km 0.621 mi, 1
. We place 1 km
400 km 0.621 mi
=
×
1 km
1
1 km
in the denominator so we can cancel km.
400 km
0.621 mi
(
)
=
×
Cancel km, the unwanted unit.
1
1 km
×
400 0.621 mi
248.4 mi
(
)
=
=
=
248.4 mi
Do the arithmetic.
×
1 1
1
Therefore: 400 km = 248.4 mi.
Ex 3 : Change 0.825 liters to milliliters.
(
)
=
×
0.825 L 0.825 L 1
Multiplying by 1 does not change the value of 0.825 L.
1000 ml
=
=
Since 1 L 1000 ml, 1
. We place L in the
0.825 L 1000 ml
=
×
1 L
1
1 L
denominator so we can cancel L.
0.825 L
1000 ml
(
)
=
×
Cancel L, the unwanted unit.
1
1 L
×
0.825 1000 ml
(
)
=
=
825 ml
Do the arithmetic.
×
1 1
Therefore: 0.825 L = 825 ml.
Sometimes it is necessary to multiply by two unit fractions in order to obtain the correct unit.
Ex 4: How many yards are in 12 miles?
(Since our conversion equations do not directly relate miles and yards, we must first convert miles
to feet, then feet to yards.)
(
)
=
×
×
12 mi 12 mi
1
1
Multiplying by 1 does not change the value of 12 mi.
5280 ft
=
=
Since 5280 ft 1 mi, 1
12 mi 5280 ft 1 yd
1 mi
=
×
×
1
1 mi
3 ft
1 yd
=
=
and 1 yd
3 ft, so 1
.
3 ft
12 mi
5280 ft
1 yd
(
)
=
×
×
Cancel mi and ft, the unwanted units.
1
1 mi
3 ft
×
×
12 5280 1 yd
(
)
=
=
21,120 yd
Do the arithmetic.
× ×
1 1 3
=
Therefore 12 mi
21,120 yd.
Revised 5/2011
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