Introduction to Chemical Principles, 11e (Stoker)
Chapter 2 Numbers from Measurements
2.1 Multiple Choice
1) Which statement contains an exact number?
A) A gross of paper contains 144 sheets.
B) One sheet of paper is 0.0042 inches thick.
C) One sheet of paper measures 8.5 x 11 inches.
D) A ream of medium weight paper weighs 20 pounds.
2) Which of the following is an inexact number?
A) There are 12 eggs in a dozen.
B) The conversion 1000 mm = 1 m.
C) This card measures 3.1 inches x 4.2 inches.
D) There are 2 cups in one pint.
3) A lab technician was assigned the task of determining the density of a sample of blood
plasma. The technician performed three replicate measurements of the density of the sample and
reported the following results.
0.810 g/mL 1.375 g/mL 2.046 g/mL
The actual density of blood plasma is 1.027 g/mL. In evaluating the technician’s job performance
in terms of accuracy and precision, it can be said that the technician ________.
A) was neither accurate nor precise
B) was both accurate and precise
C) was accurate but not precise
D) was precise but not accurate
4) Which of the following contain three significant figures?
I. 326.0 II. 0.00310 III. 46,900 IV. 1.070 V. 0.020
A) II, III and V
B) II and III
C) IV and V
D) I, III and IV
5) A lab technician was assigned the task of determining the pH of a sample of blood. The
technician performed three replicate measurements of the pH and reported the following results.
pH = 6.98 pH = 6.99 pH = 6.98
The actual pH of blood is 7.40. In evaluating the technician’s job performance in terms of
accuracy and precision, it can be said that the technician ________.
A) was neither accurate nor precise
B) was both accurate and precise
C) was accurate but not precise
D) was precise but not accurate
6) If the accepted value for the length of an object is 6.78 cm, which of the following sets of
experimental results is best described as both precise and accurate?
A) 6.78 cm, 6.38 cm, 6.48 cm (average = 6.55 cm)
B) 6.79 cm, 6.78 cm, 6.77 cm (average = 6.78 cm)
C) 6.71 cm, 6.71 cm, 6.72 cm (average = 6.71 cm)
D) 6.88 cm, 6.88 cm, 6.58 cm (average = 6.78 cm)
7) Which of the following sources of experimental error would properly be classified as a
systematic error?
A) momentary changes in air currents within the instrument room
B) accidental miscalibration of the instrument being used
C) variances in the angle from which the instrument scale is read
D) momentary changes in the temperature of the instrument room
8) Which of the following sources of experimental error can be classified as random error?
A) The balance was not properly zeroed before weighing each sample.
B) The temperature in the room is not consistent.
C) The pipet used to measure a sample was not calibrated properly.
D) None of the above
9) Which measurement is consistent with a graduated cylinder which has an uncertainty of 0.1
mL?
A) 21.14 mL
B) 21 mL
C) 21.1 mL
D) 21.140 mL
10) Which device below is the most accurate for measuring volume?
A) a beaker calibrated in 1 milliliter units
B) a graduated cylinder calibrated in 0.5 milliliter units
C) a graduated pipet calibrated in 0.1 milliliter units
D) a buret calibrated in 0.02 milliliter units
11) A balance has an accuracy of 0.001 grams. Which mass reading below was read from this
balance?
A) 49.1009 g
B) 49.10 g
C) 49.10090 g
D) 49.101 g
12) If you were recording the volume of liquid in the graduated cylinder depicted, what volume
would you record (to the correct number of significant figures)?
A) 25.700 mL
B) 25.7 mL
C) 25 mL
D) 25.70 mL
13) If you were recording the volume of liquid in the pipet depicted, what volume would you
record (to the correct number of significant figures)?
A) 4.557 mL
B) 4.56 mL
C) 5 mL
D) 4.6 mL
14) Which of the following statements concerning the “significance” of zeros in recorded
measurements is incorrect?
A) leading zeros are never significant
B) confined zeros are always significant
C) trailing zeros are not always significant
D) trailing and leading zeros are not always significant
15) Which one of the following numbers contains 4 significant figures?
A) 6.43
B) 39.4
C) 0.04840
D) 0.0257
16) In which one of the following numbers are none of the zeros significant?
A) 298.010
B) 3100
C) 0.00001470
D) 2.70400
17) In which of the following pairs of numbers does each member of the pair contain the same
number of significant figures?
A) 39 and 3090
B) 9900.0 and 60.01
C) 0.05700 and 0.0570
D) 45010 and 0.09871
18) Which of the following numbers contains 2 significant figures?
A) 3.741
B) 190
C) 0.02
D) 90.60
19) How many of the following numbers has 4 significant figures?
19.00 0.00006 1.609 x 108 13,600
A) 0
B) 1
C) 2
D) 3
20) A balance has an accuracy of ±0.01 grams. A beaker weighed 15 grams when weighed on
this balance. Using the correct number of significant figures, the weight of the beaker should be
recorded as ________.
A) 15.000 g
B) 15 g
C) 15.0 g
D) 15.00 g
21) Which of the following numbers contains three significant figures?
A) 1.050
B) 85.967
C) 8.90
D) 350
22) The number 0.090804, when rounded off to 4 significant figures, would appear as ________.
A) 0.091
B) 0.0908
C) 0.09080
D) 0.090
23) The number 80710, when rounded off to 2 significant figures, would appear as ________.
A) 80700
B) 81000
C) 8100
D) 8070
24) When the number 0.0047896 is rounded to two significant figures it would appear as
________.
A) 0.00479
B) 0.004790
C) 0.0048
D) 0.0050
25) What are the correct number of significant figures in the answer for the following sum:
8.650 + 19.6 + 44.05 + 88
A) 2
B) 3
C) 4
D) 5
26) The calculator answer obtained from multiplying 21.08 x 1.9634 is 41.388472. The answer
to the correct number of significant figures is ________.
A) 41.388
B) 41.4
C) 41.39
D) 41.3884
27) The correct answer obtained from subtracting 1.2 from 123.96 contains ________.
A) 2 significant figures
B) 3 significant figures
C) 4 significant figures
D) 5 significant figures
28) Do the following calculation. How many significant figures are justified for the answer?
5.02 + 6.119 + 0.04117
A) 4
B) 3
C) 5
D) 7
29) The correct answer for the calculation
where 126 and 135 are counted numbers and 1.364 and 0.8951 are measured numbers is
________.
A) 1.422
B) 1.4
C) 1.42
D) 1.4220
30) Do the following calculation and express the answer using the correct scientific notation:
A) 6.34 x 1021
B) 1.58 x 10-22
C) 6.34 x 10-2
D) 15.8
31) Perform the following mathematical operation, and express the answer to the correct number
of significant figures.
12.47 g
1.026 g
135.8 g
A) 149.296
B) 150.
C) 149.3
D) 149.30
32) The numerical value for (5.6 x 104) ÷ (7.89 x 102) is, with the proper number of significant
figures, equal to:
A) 70.976
B) 71
C) 7.098 x 101
D) 71.0
33) Carry out the following calculations. Express your answer to the proper number of
significant figures: (21.648 + 89)/0.00201
A) 55223
B) 55220
C) 55000
D) 55200
34) Which of the following statements is true?
1. 0.0206
2. 81.30
3. 29007
4. 123,000
5. 906.0
6. 300
A) Numbers that contain three significant figures are 1, 3, and 6.
B) Numbers in which all zeros are significant are 2, 3, 4, and 5.
C) Numbers in which none of the zeros are significant are 1 and 2.
D) Number with one significant figure is 6.
35) A rubber band is found to weigh 0.0978 g. What is the total mass of 106 such identical
rubber bands?
A) 10.37 g
B) 10.367 g
C) 10.4 g
D) 10. g
36) Perform the following mathematical operations. Express your answer to the proper number
of significant figures. (93.789 − 5.40) x 18.057 =
A) 1600
B) 1596.239
C) 1590
D) 1596.0
37) A student cut 1200 pieces of copper wire, each weighing 1.769 grams. Calculate the total
mass of the pieces of copper to the correct number of significant figures.
A) 2123
B) 2100
C) 2120
D) 2122.8
38) A penny weighs 1.575g. What is the total mass of 150 pennies?
A) 236.25
B) 236.2
C) 236
D) 240
39) The average mass of a Vitamin C tablet is 0.653 g. What would be the total mass of 125
tablets?
A) 81.625 g
B) 81.6 g
C) 81.62 g
D) 82.0 g
40) Water and vitamin C were added to a beaker. Calculate the mass of the beaker and its
contents, and choose the answer with the appropriate number of significant figures.
146.20 g beaker + 23.1 g water + 0.34 g vitamin C =
A) 169.64 g
B) 169 g
C) 169.6 g
D) 170 g
41) What mathematical operation is represented by the exponential notation of 10−4?
A) 10 x 10 x 10 x10
B) 10 + 10 + 10 + 10
C) 1/10 x 1/10 x 1/10 x 1/10
D) 1/10 + 1/10 + 1/10 + 1/10
42) The number 3009.1 expressed in scientific notation to the correct number of significant
figures becomes ________.
A) 3.01 x 103
B) 3.009 x 104
C) 3.0091 x 10−3
D) 3.0091 x 103
43) The number 0.00309 expressed in scientific notation to the correct number of significant
figures becomes ________.
A) 3.090 x 103
B) 3.09 x 10−3
C) 3.09 x 103
D) 3.090 x 10−4
44) The number 12.68 x 102, when expressed in correct scientific notation, becomes ________.
A) 1268 x 104
B) 0.1268 x 100
C) 1.268 x 103
D) 1.268 x 10−3
45) When 0.0005760 is written in proper scientific notation with the correct number of
significant figures the number is:
A) 57.60 x 10-5
B) 5.760 x 10-4
C) 5.760 x 104
D) 5.76 x 10-4
46) What is the correct exponential term for the following mathematical operation?
A) 10−6
B) 102
C) 10−2
D) 10−4
47) How many numbers will be in the coefficient when 0.0090110 is expressed in scientific
notation?
A) 2
B) 3
C) 4
D) 5
48) The number 1.987 x 106 in normal decimal notation is ________.
A) 1,987,000
B) 198,700
C) 19,870
D) 19,870,000
49) The number 9080000 written in scientific notation to the correct number of significant
figures is ________.
A) 9.1 x 107
B) 9.08 x 107
C) 9.08 x 106
D) 9.1 x 106
50) The number 7.134 x 107 in normal decimal notation is ________.
A) 0.0000007134
B) 7,134,000
C) 713,400
D) 71,340,000
51) Which one of the following mathematical expressions is not evaluated correctly?
A) 10−3/106 = 10−9
B) 108/106 = 102
C) 10−2/10−4 = 102
D) 10−3/10−6 = 109
52) The correct answer obtained by dividing 4.65 x 105 by 9.4 x 10−2 together is ________.
A) 2.0 x 10−7
B) 2.02 x 10−7
C) 4.9 x 106
D) 4.95 x 106
53) The correct answer obtained by dividing the measurement (6.00 x 104) by the measurement
(2.0 x102) is ________.
A) 3 x 101
B) 3 x 10−2
C) 3.00 x 102
D) 3.0 x 102
54) Perform the indicated mathematical operations and express the answer in scientific notation
rounded off to the proper number of significant figures.
[2.098 x 1014 /74.5 x 10-6] (1.0900 x 104)
A) 3.0696 x 1022
B) 3.0696 x 10−23
C) 3.1 x 1023
2.2 Short Answer
1) A pipet is calibrated with the smallest scale markings of 0.1 milliliters. Indicate to what
uncertainty readings should be recorded for measurements made with this device.
2) For each of the measurements on the left, determine the number of significant figures present.
A)
1.0010
________
B)
30901
________
C)
620200
________
D)
0.02060
________
3) How many significant figures are found in each of the following measurements?
A)
300 grams
________
B)
0.0207 pounds
________
C)
66,900,000 miles
________
D)
20.10 liters
________
4) Do the following multiplications and divisions, expressing your answers to the proper number
of significant figures.
A) 86.40/12.095 ________
B) (2.00 x 102) x (2.00 x 10-4) ________
C) (7.0 x 10-6) x (3.00 x 104) ________
D) (8.00 x 106)/(4.00 x 104) ________
5) Do the following additions or subtractions, expressing your answers to the proper number of
significant figures.
A) 4.63 + 7.014 − 1.200 ________
B) 200 + 0.09 ________
C) 3.070 − 3.050 ________
D) (6.3 x 107) + (4.5 x 103) ________
6) Round off each of the following numbers to 3 significant figures.
A) 397.48 ________
B) 145,120 ________
C) 0.00860 ________
D) 1900 ________
7) Round off the following numbers to 4 significant figures.
A) 398.845 ________
B) 245,864 ________
C) 0.00065298 ________
D) 15000 ________
8) For each of the calculator-completed calculations on the left, determine the correct number of
significant figures that the answer should have.
A)
3.54 2.17 = 7.6818
_______
B)
231 + 23.42 = 254.42
_______
C)
273.2 − 33 = 240.2 (33 is an exact number)
________
D)
6.00/2.0 = 3
_______
9) Round off each of the following numbers to the number of significant figures indicated in
parenthesis.
A) 652,387 (two)
B) 431.50 (three)
C) 0.003010 (two)
D) 0.45 (one)
10) Round off each of the following numbers to the number of significant figures indicated in
parenthesis.
A) 652,387 (two)
B) 431.50 (three)
C) 0.003010 (two)
D) 0.45 (one)
11) Perform the following mathematical operations and express the answers to the correct
number of significant figures.
A) 74.632 + 23 − 1.01 =
B) [(3.9780 x 10-2) x (1.010 x 104)]/ [(3.290 x 10-5) x (7.85 x 102)] =
C) [(2.1 x 10-4/6.89 x 10-3)] – (1.59 x 10-2) =
D) [400 x 1719]/[56.1 x 97] =
E) [10-7 x 106 x 104] / [10-5 x 109] =
F) (235.8 + 15940 + 6.17) /1.987 =
12) Express the following numbers in scientific notation.
A)
6,473
________
B)
0.0004081
________
C)
6,970,000
________
D)
0.00021
________
13) Express the following numbers in scientific notation:
A) 5489 ________
B) 0.0000653 ________
C) 623,000,000 ________
D) 0.005300 ________
14) Convert the following numbers from scientific notation to ordinary decimal notation.
A) 3.01 x 10−3 ________
B) 9.0 x 10−3 ________
C) 9.91 x 105 ________
D) 6.429 x 108 ________
15) Express the following exponential expressions in correct scientific notation.
A) 430 x 10−2 ________
B) 13.30 x 108 ________
C) 0.000330 x 10−2 ________
D) 0.123 x 106 ________
16) Using scientific notation, express the number five million five hundred thousand to 4
significant figures.
17) Using scientific notation, express the number four thousand three hundred fifty to 3
significant figures.
18) Perform the following mathematical operations. Express your answer to the proper number
of significant figures.