MATH 11008:
Metric System
• Length: measured in meters m which is about 39.37 inches
one meter: is 1,650,763.73 times the wavelength of orange-red light emitted by the
atoms of the gas krypton 86.
Prefixes to know:
◦ milli- means
1
1000
◦ deka- (deca-) means 10
◦ centi- means
1
100
◦ hecto- means 100
◦ deci- means
1
10
◦ kilo- means 1000
Note: can easily convert from one to another by moving the decimal point.
Example 1: Convert the following.
dm
(a) 45.78 mm =
(b) 5.93 m =
cm
(c) 27.3 dm =
(d) 0.0453 km =
hm
m
2
MATH 11008: METRIC SYSTEM
• Area: measured in square meters m2
Question: How many square centimeters cm2 are in one square meter m2 ?
Note: Can convert from one to another by moving the decimal point.
Example 2: Convert the following.
(a) 26.7 mm2 =
(b) 9.3 m2 =
dm2
cm2
(c) 47 dm2 =
(d) 0.0453 km2 =
hm2
m2
MATH 11008: METRIC SYSTEM
3
• Volume: measured in liters L. One liter is a little more than a quart.
one liter: is the volume of a cube that measures 10 cm on an edge.
Note: Can convert from one to another by moving the decimal point.
• Mass: measured in kilograms kg
one kilogram: is the mass of 1 liter of water in its densest state. (1 kg is about 2.2
pounds).
cube
volume
mass (water)
1 m3
1 kL
1 tonne (metric ton)
1 dm3
1L
1 kg
1 cm3
1 mL
1g
Note: can convert from one to another by moving the decimal point.
• Temperature: measured in Celsius.
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MATH 11008: METRIC SYSTEM
English and Metric Conversions
• 1 yd = 0.9144 m
• 1 gal = 3.785 L
• 1 mi = 1.609 km
• 2.2 lbs = 1 kg
• 1 in = 2.54 cm
9
• F = C + 32
5
Example 3: Perform the following conversions. Use a calculator where necessary. Round
answers to four decimal places.
(a)
19 ft to m
(b)
16 L to qts
(c)
8.5 lbs to kg
(d)
50◦ C to
◦
F
MATH 11008: METRIC SYSTEM
5
EXERCISES
Convert the following measures:
1.
12 m =
2.
46780000 mm =
3.
89000 cm =
4.
562 hm =
5.
6.
7.
km
m
dam
57 dg =
9.
32 g =
13.
5 m2 =
14.
16 dm2 =
15.
56000 cm2 =
16.
1200000 mm2 =
17.
5 m3 =
18.
5.6 dm3 =
19.
56000 cm3 =
mL
mm2
cm2
m2
km
3.567 dam =
8.
2.36 kL =
mm
13.45 dm =
475 cg =
12.
cm2
hm
mm3
mg
cm3
hg
mg
10.
520 L =
kL
20.
1200000 mm3 =
11.
56 mL =
L
21.
73 km3 =
m3
dam3
dam3
Perform the following conversions. Round answers to four decimal places.
22. 786 yd to meters
26. 14.5 L to qts
23. 130 mi to km
27. 16 gal to L
24. 2350 g to lbs
28. 25 km to mi
25. 54.3 lb to g
29. 75 in to m
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MATH 11008: METRIC SYSTEM
30. 9.5 lbs to kg
34. 75◦ F to
◦
C
31. 17.3 kg to lbs
35. 25◦ C to
◦
F
32. 20 qts to L
36. 212◦ F to
33. 60◦ C to
◦
F
37. 50◦ C to
◦
◦
C
F
MATH 11008: METRIC SYSTEM
7
ANSWERS
1.
12 m = .012 km
2.
46780000 mm = 46780 m
3.
89000 cm = 89 dam
4.
562 hm = 56200000 mm
5.
13.45 dm = .001345 km
6.
3.567 dam = .3567 hm
7.
475 cg = 4750 mg
8.
57 dg = .057 hg
9.
32 g = 32000 mg
10.
520 L = .52 kL
11.
56 mL = .056 L
12.
2.36 kL = 2360000 mL
13.
5 m2 = 5000000 mm2
14.
16 dm2 = 1600 cm2
15.
56000 cm2 = 5.6 m2
16.
1200000 mm2 = 12000 cm2
17.
5 m3 = 5000000000 mm3
18.
5.6 dm3 = 5600 cm3
19.
56000 cm3 = .056 m3
20.
1200000 mm3 = .0000012 dam3
21.
73 km3 = 73000000 dam3
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.