CONVERTING UNITS
Many students are intimated when they have to convert units in a problem. However if you use a systematic approach this is not hard. Here is the approach I suggest. First, some basic rules:
1) Always carry the units along in your problems, this way the units do not get separated from the numbers. Use a clean sheet of paper to work a problem and work down from the top to the bottom in an organized way.
2) Always set up the problem on paper first before trying to use a calculator to get an answer.
To convert units, we use a Conversion factor which has a value equal to 1. So, for example, to convert three dozen eggs into the actual number of eggs
3 dozen eggs x [1] = 3 dozen eggs
3 dozen eggs x [C.F.] = 3 dozen eggs; so long as C.F. = 1
3 dozen eggs x [12 eggs/1 dozen eggs] = 36 eggs; since 12 eggs = 1 dozen
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Try converting miles to kilometers. You need to know that 1.6 km = 1 mile
12 miles x [1] = 12 miles
12 miles x [C.F.] = 12 miles; so long as C.F. = 1
12 miles x [1.6 km/mile] = 19 km;
since 1.6 km = 1 mile; the C.F. [1.6 km/mile] = 1
Sometimes, it is easiest to use two conversion factors when you don’t know the conversion factor to use in one step.
Try these problems:
Convert--
a)14. 4 feet into inches
b)15 years into days
c) 4.5 x 103 metric tons (mt) into kilograms
d) 4.5 x 103 metric tons (mt) into pounds (lbs)
e) 1.65 x 105 days into years
f) 4.7 x 102 metric tons (mt) into kilograms
g) 6.5 tg into kilograms
1 inch = 2.54 centimeter (cm)
1 mile = 5280 feet
1 year = 365 days
1 metric ton = 1000 kilograms (kg)
1 kilograms (kg) = 2.2 pounds
1 kilogram (kg) = 103 grams
1 teragram (tg) = 1012 grams
I strongly recommend that you do these problems first before looking at the answers below.
Answers:
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Initial Value |
x CF#1 |
x CF#2 (if needed) |
Final Value |
|
a |
14.4 feet |
12 inches foot |
- |
172.8 inches or 1.73 x 102 inches |
b |
15 years |
365 days year |
- |
5475 days or 5.48 days |
c |
4.5 x 103 mt |
103 kg mt |
- |
4.5 x 106 kg |
d |
4.5 x 103 mt |
103 kg mt |
2.2 lbs/kg |
9.9 x 106 lbs |
e |
1.65 x 105 days |
1 year 365 days |
- |
452 years or 4.52 x 102 years |
f |
4.7 x 102 mt |
1000 kg 1 mt |
4.7 x 105 kg |
|
g |
6.5 tg |
1012grams tg |
1 kg 1000 grams |
6.5 x 109 kg |