Metric and Measurement
Name: ________________________
5.0 Chemistry I
Date: ______________ Period: ____
Metric Units and Prefixes
1. The basic SI unit for measuring length is the meter. Using metric prefixes from our notes,
give the appropriate unit for measuring the following quantities.
Example: the distance between two cities
kilometers
A. the distance between your eyes
___________________________
B. the diameter of wire used to make a paper clip
___________________________
C. the length of a football field
___________________________
D. the thickness of a piece of paper
___________________________
2. The basic SI unit for measuring mass is the kilogram. Using metric prefixes from our notes,
give the appropriate unit for measuring the following quantities.
Example: the mass of a person
kilograms
A. the mass of an aspirin tablet
___________________________
B. the mass of the Empire State Building
___________________________
C. the mass of an apple
___________________________
D. the mass of an automobile
___________________________
3. A non-SI unt frequently used to measure volume is the liter. Using metric prefixes from our
notes, give the appropriate unit for measuring the following quantities.
Example: the volume of an eyedropper
milliliters
A. the volume of water in a bathtub
___________________________
B. the volume of a can of soda
___________________________
C. the volume of a swimming pool
___________________________
D. the volume of a microwave oven
__________________________
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Metric Conversions
4. Convert 83 cm to meters.
5. Convert 459 L to milliliters.
6. Express 1123 pg in nanograms.
7. Express 0.032 m3 in liters.
8. Express 2.5 mm in micrometers.
9. Which is a smaller amount of time, 1351 ps or 1.2 ns? Explain your answer with
calculations.
10. Which is a larger pressure, 232.1 kPa or 125,487 Pa? Explain your answer with
calculations.
11. Which is the smaller mass, 285.0 cg or 23.78 dg? Explain your answer with calculations.
12. Which is the shorter length, 175.6 mm or 38.4 cm? Explain your answer with calculations.
13. Convert the following masses into grams.
a. 0.7824 mg
b. 345, 000 ng
2
c. 0.00378 kg
d. 34,981 g
Exact Numbers vs. Uncertainty in Measurement
14. Which of the following quantities can be determined exactly?
a) The number of light switches in the room
b) The number of ounces in one pound
c) The number of stars in the sky
d) The number of inches in a foot
e) The number of red blood cells in exactly one quart of blood
3
15. Measuring Liquid Volume: write the answers to the correct precision for each graduated cylinder.
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16. Read the level of the liquid in each of these graduated cylinders to the correct precision.
Remember to read the volumes at the meniscus.
Water: ________________________
Mercury: ________________________
(Note: Mercury has an inverted meniscus)
17. Using a ruler - Write the answers to the correct precision for the ruler.
a.
__________________
b.
__________________
18. Triple Beam Balance - Write the answers to the correct precision for the triple beam balance.
_______________
19. An electronic balance shows the mass of a sample of sodium chloride to be 29.732 g. What
is the uncertainty of the measurement? _________________
In what range can the true
value exist? ________________________________________________________________
5
20. Measuring Temperature: Write the answers to the correct precision for each thermometer.
6
Scientific Notation
21. Express the following in scientific notation:
a) 1,000
__________________
h) 640,000
__________________
b) 0.0001
__________________
i) 0.089
__________________
c) 10,000
__________________
j) 66,000
__________________
d) 0.0000024
__________________
k) 0.0000403
__________________
e) 0.0000001
__________________
l) 104,000
__________________
f) 10,000,000
__________________
m) 90,000
__________________
g) 13,000
__________________
n) 0.0000764
__________________
22. Express the following in regular notation:
a) 104
________________________
i) 1011
________________________
b) 10-6
________________________
j) 106
________________________
c) 102
________________________
k) 10-5
________________________
d) 107
________________________
l) 10-16
________________________
e) 6.1 x 106 ______________________
m) 8.88 x 10-12 ____________________
f) 5.47 x 103 ____________________
n) 2.22 x 10-4 ____________________
g) 1.11 x 104 ____________________
o) 7.07 x 106 ____________________
h) 8 x 10-5 ______________________
p) 6.00 x 10-3 ____________________
23. Perform the calculations below. Then express your answers in scientific notation.
a) Multiply 7 x 10-3 by 1.2 x 109.
b) Divide 3.6 x 102 by 4.8 x 104.
c) Add 8.75 x 104 to 2.513 x 105.
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d) Subtract 3.6 x 10-3 from 4.5 x 10-4.
e) Multiply 7.2 x 10-2 by 5.1 x 103.
Significant Digits
24. Determine the number of significant digits in each of the following measurements.
a) 6.751 g
_____
k) 43.07 cm
_____
b) 0.157 kg
_____
l) 2.690 g
_____
c) 28.0 mL
_____
m) 0.002300 mg _____
d) 2500 m
_____
n) 2500.0 cm
_____
e) 0.070 g
_____
o) 0.189 mL
_____
f) 30.07 g
_____
p) 144.07 g
_____
g) 0.106 cm
_____
q) 40.319 hg
_____
h) 0.0067 g
_____
r) 48.57193 daL _____
i) 26.509 cm
_____
s) 0.1209 m
_____
j) 0.0230 cm
_____
t) 54.52 mL
_____
25. Express the results of each of the following calculations to the correct number of significant
figures. Assume that the numbers in these calculations are inexact and are obtained from
measurements.
a. 3.20 g + 0.03 g
_________________
d. 110 s – 1.3 s
b. 4302 g + 0.837 g
_________________
e. 5.7 cm x 0.20 cm __________________
c. 100. cm – 1.6 cm
__________________ f. 10.2 s  0.4 s
___________________
__________________
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26. The following problems have been performed on a calculator. Rewrite the answers so that
they have the correct precision. One answer is correct.
a) 1.25 g x 8.6 C = 10.75 gC
________________
b) 100.00 g 
________________
25.0 mL = 4 g/mL
c) 500.00 cm x 40.00 cm = 20,000 cm2
________________
d) 38 cm + 5.100 cm + 4.13 cm = 47.23 cm
________________
e) 716.55 g – 0.005 g = 716.545 g
________________
f) 28.00 g  85.2 cm = 0.3286385 g/cm3
________________
g) 8.000 km – 0.54 km = 7.46 km
________________
h) 23.18 m + 6.819 m = 29.999 m
________________
27. Perform the following operations. Express your answers with the correct number of
significant digits.
a) 16.5
+
b) 13.25
8
+
10.00
+
+
4.37
=
______________
9.6
=
______________
c) 23.27 –
12.058
=
______________
d) 13.57 –
6.3
=
______________
e) 2.6
×
3.78
=
______________
f) 6.54
×
0.37
=
______________
g) 0.058 ÷
2.10
=
______________
h) 39
24.2
=
______________
14.369
=
______________
______________
÷
i) 27.68 –
j) 0.085
×
0.05
×
0.655 =
k) 0.0853
+
0.0547
+
0.0370
l) 0.075
÷
0.030
+
=
0.00387
=
______________
______________
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Metric conversions using Factor Label
28. How many kilometers are there in 100 meters?
29. How many milliliters are there in 0.500 liter?
30. How many milligrams are there in 10.0 kilograms?
31. How many deckameters are in 250. centimeters?
32. How many decimeters are in 50. kilometers?
33. Determine the number of decigrams equal to 4550.0 milligrams.
34. How many micrograms are there in 10.5 kg?
35. Convert 540 nm to kilometers.
36. A macaroni and cheese box has the following dimensions: 9.75 cm long, 18.50cm high, and
2.92 cm width. Calculate the volume in m3.
10
Factor-Label Practice Problems – Perform the following calculations using factor label. Use
the correct number of significant digits in your answer.
37. How many gallons are in 2.5 liters?
38. How many joules are in 341 calories?
39. How many feet are in 0.500 mile?
40. How many seconds are in 18.0 minutes?
41. How many seconds are in 10.5 days?
42. How many days are in 12,583 seconds?
43. Convert 36.7 miles to kilometers.
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44. Convert 47.8 inches to centimeters.
45. Convert 35,978 calories into joules.
46. Convert 0.9831 atmospheres to pascals.
47. Convert 10 kilometers into miles.
48. Convert 31.2 decimeters into inches.
49. Convert 1200 dm3 to m3.
50. Convert 0.49 cm2 to mm2.
51. Convert 0.035m3 to cm3.
52. Convert 15 km/h to m/s.
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Density - Perform the following calculations using factor label. Use the correct number of
significant digits in your answer.
53. A block of aluminum has a mass of 36.40 g and a volume of 13.5 cm3. What is the block’s
density?
54. The density of CCl4 (carbon tetrachloride) is 1.58 g/mL. What is the mass of 95.7 mL of
CCl4?
55. What is the volume of 227 g of olive oil if its density is 0.92 g/mL?
56. Calculate the density of a piece of metal if its mass is 201.0 g and its volume is 18.9 cm3?
57. The density of a block of ice is 0.917 g/cm3. How much volume (in mL) does 52.3 g of ice
occupy?
58. The density of air is 1kg/m3. What is the density of air in g/cm3?
59. The density of water is 1.0 g/cm3. What is the mass of water in kilograms in a bathtub whole
volume is 3 m3?
60. Equal amounts of three liquids – carbon tetrachloride (D = 1.58 g/cm3), mercury (D = 13.546
g/cm3), and water (D = 1.00 g/cm3) – are mixed together. After mixing, they separate to
form three distinct layers. Draw and label a sketch showing the order of the layers in the test
tube.
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To determine the density of a copper alloy wire, a student first found the mass of each of five
pieces of the wire on an electronic balance. The masses are recorded in the table below. Then
the five pieces of wire were placed into a graduated cylinder approximately half filled with
water. The initial and final volumes are shown below in the picture.
Using this information, answer the questions below. Be sure to write all numbers to the
correct number of significant digits following the rules, and include a unit on every number.
You must show your work!
61. Determine the combined mass of the metal wires.
62. Determine the total volume of the metal wires.
63. Find the density of the copper alloy.
Temperature Conversions
64. Convert Celsius temperatures to Kelvin and Kelvin temperatures to Celsius.
a. 13.21°C
b. 743.0 K
c. 115 K
d. −39.9°C
e. 1209.84 K
f. 208°C
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Metric and Measurement Review
65. Express the following numbers in scientific notation or regular form:
a. 8960
_______________
f. 4.563 x 107
__________________
b. 0.000 23
_______________
g. 2.53 x 10-3
__________________
c. 86,000
_______________
h. 6.805 x 108
__________________
d. 36,000,000
_______________
i. 5.6 x 10-2
__________________
e. 0.000 000 025 3 _______________
j. 3.29 x 104
__________________
66. Identify and write the number of significant digits in each of the following measurements:
a. 520 mL
____
g. 0.057 g
____
m. 0.001 cm
____
b. 0.0102 ns
____
h. 5.017 L
____
n. 0.0010010
____
c. 0.230 kg
____
i. 8000 km
____
o. 328.46 mm
____
d. 25,600 L
____
j. 0.05030
____
p. 0.00607 cm3
____
e. 230.005 m
____
k. 10.002 ns
____
q. 610.0 kPa
____
f. 109,000 kg
____
l. 0.451 Pa
____
Perform the following calculations. Use the correct number of significant digits in your answer.
67.
0.3287 cm
x
45.2 cm =
68.
125.5 kg + 52.68 kg + 2.1 kg =
69.
52.8 Pa + 3.0025 Pa

253.4 Pa
70.
(0.12 cm + 5.16 cm) x (93.0 cm - 45.56 cm) =
71.
68.32 ns + (-1.001 ns) + (-0.00367 ns) + (-678.1 ns) =
72.
0.258 mL  0.36105 mL =
15
73.
(1250 - (234.207  52.69)) =
74.
78.26 - 89.50
=
678.2 + 9511
75.
Explain why the least reliable digit in a measurement is always the final digit.
76.
Convert 18.5 mm to km.
77.
Convert 350 mm to km.
78.
Convert 20 dag to cg.
79.
Convert 542 cm3 to L.
80.
Convert 72.8 dL to mL.
81.
Convert 54 cm2 to m2.
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82.
What is the density in lb/cm3 of a substance with a mass of 15 kg and a volume of 4.6 mL?
83.
What is the mass of an object with a density of 1.84 g/mL and a volume of 24 mL?
84.
What is the volume of an object with a density of 5.6 g/mL and a mass of 86 g?
85.
Find the volume of a cereal box that is 35.2 cm high, 22.0 cm wide and 60. mm deep.
86.
According to legend, a king once requested that the royal scientist, Archimedes, determine
if his crown was really made of solid gold. Archimedes measured the mass of the crown.
He used water displacement to calculate its volume. If the mass of the crown was 505,431
mg, and the volume was 44.0 mL, what was the density of the crown? If the density of
pure gold is 19.3 g/cm3, was the crown solid gold?
87.
Light travels at a speed of 2.99792458 x 108 meters per second. The distance light travels
in one year is called a light year. How many meters are equal to one light year? How
many feet are in one light year? (show your work!)
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88.
In an Olympic speed skating event, the winner skated 1500. meters in 2 minutes and 2.96
seconds. Express this in km/hr.
89.
If a car gets 22.0 miles per gallon, what is this in km/L?
90.
A man raised 50 goats, and then entered into a series of transactions. He traded all the
goats for sheep at an exchange rate of 5 goats for 7 sheep. He then traded all the sheep for
hogs at a rate of 4 sheep for 2 hogs, each weighing 250 pounds. He sold all the hogs at a
market price of $44.00 per 100 pounds. How much money did he make from the sale of
the goats?
4) 0.83m 5) 459,000mL 6) 1.123ng 7) 32L 8) 2500m 9) 1.2ns 10) 232.1kPa 11) 23.78dg 12) 175.6mm 13a) 7.824x10 -4g
b) 3.45x10-4g c) 3.78g d) 0.034981g 23a) 8.4x106 b) 7.5x10-3 c) 3.388x105 d) -3.15x10-3 e) 3.672x102 24a) 3.23g c) 98cm
e) 1.1cm2 27a) 29 d) 7.3 g) 0.028 j) 0.003 28) 0.1km 29) 500.mL 30) 1.00x107mg 31) 0.250dam 32) 5.0x105dm
33) 45.500dg 34) 1.05x1010μg 35) 4.4x10-10km 36) 5.27x10-4m3 37) 0.66 gal 38) 1430 J 39) 2,640 ft 40) 1080 s 41) 9.07x105s
42) 0.14564 days 43) 59.1km 44) 121cm 45) 150,530J 46) 9.961x104Pa 47) 6mi 48) 123in 49) 1.2m3 50) 49mm2
51) 3.5x104cm3 52) 4.2m/s 53) 2.70g/cm3 54) 151g 55) 250mL 56) 10.6g/cm3 57) 5.70mL 58) 0.001g/cm3 59) 3000kg
63) 9.17g/mL 66) 14.9cm2 67) 180.3kg 68) 0.220 69) 250.cm2 70) -610.8ns 71) 0.715 72) 1250 73)-0.001103 75) 1.85x10-5km
76) 3.5x10-4 77) 20,000cg 78) 0.542L 79) 7280mL 80)0.0054m2 81) 7.2lb/cm3 82) 44g 83)15mL 84) 4.6L 85) no
86) ~9.5x1015m, ~ 3.1x1016ft 87) 43.92km/hr 88) 9.31km/L 89) $4812.50
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