NAME ___________________________________
NOTES: UNIT 1 (2): MEASUREMENT
I) MEASUREMENT, SIGNIFICANT FIGURES & CALCULATIONS
A) Accuracy vs. Precision
1) Accuracy (“correctness”): This refers to the closeness of a lab measurement or calculation,
relative to an accepted (or a theoretical) value.
a) In lab the level of accuracy is designated in a number of ways:
i. finding an average value
ii. recording a measurement and indicating a ± range: e.g. 12.35 mL
iii. calculating the percent difference or percent error
±0.01 mL
e.g. The water of hydration for CuSO45H2O, is theoretically 36.1%. Were you to determine a laboratory
value of 49.0%, would your measurement be deemed “accurate”?
2) Precision: (coherence or repeat-ability): This refers to the agreement among the numerical
values of a set of measurements (or calculations) you make in lab
a) We repeat experiments (or perform multiple trials) in order to determine precision.
e.g. The water of hydration lab is repeated 3 times with the results: 47.9%, 12.5 %, and 31.3 % Are the
measurements precise, based upon the given definition?
b) In chemistry, our goal is to make measurements &/or make calculations that are BOTH
accurate AND precise.
3) Your text offers a nice metaphor for accuracy and precision. Imagine a dart board ... the
bulls-eye represents the accepted value.
Draw in 3 or 4 “darts”
(or dots, or boxes or x’s etc...) on the above diagrams that illustrate:
PRECISION but no ACCURACY
PRECISION & ACCURACY
Neither PRECISION
nor ACCURACY
63
QUESTIONS : Evaluate each situation for accuracy and precision, by stating whether you think the situation
demonstrates / lacks accuracy and whether it demonstrates/lacks precision.
1) A student experimentally determined the melting point of a substance and recorded her data. The accepted
value for the melting point is 58.7 C
Trial Melting Point
(C)
1
42.5
2
42.3
3
42.7
2) A student experimentally determined the water of hydration of a hydrate. The accepted value for the
water of hydration is 23.7%
Trial Water of Hydration
(%)
1
23.7
2
23.8
3
23.7
3) A student experimentally determined the melting point of a substance and recorded her data. The accepted
value for the melting point is 68.5C
Trial Melting Point
(C)
1
78.2
2
50.0
3
60.7
4) Study the data in question 3). Submit data that would demonstrate precision, but no accuracy.
Trial Melting Point
(C)
1
2
3
64
B) A measurement is different from a number!
1) A measurement should have 3 attributes:
appropriate magnitude, a unit and the correct # sig figs



2) appropriate magnitude: the size of a value [tens, hundreds, thousands…]
a) Be careful when you round to a particular number of significant figures … students
often round to an incorrect magnitude…. more on this later.
b) probable units:
(see Table D of your Reference Charts)
Dimension
unit (SI§ &/or related metric)
volume
mass
length
pressure
thermal energy
temperature
m3, L, mL (1 mL = 1 cm3)
kg, g, mg
m, km, , cm, mm, Å, nm, pm
kPa, atm (atmosphere)
kJ, J (for joule)
K, C
§Le
Système international d'unités is the modern form of the metric system.
Check out: http://en.wikipedia.org/wiki/International_System_of_Units
Check out: http://antoine.frostburg.edu/chem/senese/101/thermo/
c) correct number of significant figures: When a measurement is recorded, it includes
all the digits that are certain, plus one estimated (& relatively uncertain) digit.
These certain digits and plus the one uncertain digit are referred to a significant
figures. The more digits that can be legitimately recorded with a tool, the less the
relative uncertainty there is in the measurement.
When taking a measurement a scientist reads the device as far as s/he can and then
estimates on more place (digit) when appropriate. These digits are significant figures.
 it is appropriate when using burets, pipets, graduated cylinders, rulers and
thermometers to estimate to the next division in order to glean as many sig figs
as possible. This next division is imaginary ... that is you need to break up the
space between markings into 10 smaller divisions. N.B. With electronic
equipment (e.g. electronic balances) we cannot estimate to the next place on
the electronic balances.
 measurements are FINITE, because the tools we use to make those measurements are
limited. Thus, any calculated values based upon those finite measurements must
themselves be limited.
See: http://student.ccbcmd.edu/~cyau1/WhatMeaningBehindSigFig.htm or http://tinyurl.com/2fqxeu7
65
QUESTIONS:
____1) Which set of measurements are all consistent with the metric ruler shown below?
HINT: Before answering, determine how far you can read the ruler based upon its divisions, and then estimate one more place.
a) 4.50 cm,
1.500 cm,
3.45 cm
b) 1.5 cm,
1.55 cm,
2.35 cm
c) 2.400 cm, 3.40 cm,
4.75 cm
d) 1.7 cm,
1 cm,
2.40 cm
e) 1.50 cm,
1.55 cm,
2.35 cm
2) Given the graph: Lake Elevation as a function of Time
A student wrote that the level of the
1968 delta was close to 345.900 m.
Is this reading a reasonable response
given that the y-axis divisions are in 5
meter increments?
Defend:
3) Given the diagram representing a portion a graduated cylinder, record the volume, in mL, by reading the
bottom of the meniscus.
(Did you include an estimated digit?)
23
22
21
66
4) Record the length of the arrow:
___________________cm
(Did you include an estimated digit?)
5) Record the volume based upon the image of a partial graduated cylinder.
(Did you include an estimated digit???)
____________ mL
7) Given the graph of whatever the heck it says...
A student reported that the domains
with keyword at a ranking of 4.5
equaled 499.2
Is this reading a reasonable response
given that the divisions of the y-axis
are 100 intervals?
8) Given the bar graph:
Is the value for PLC systems
(5.9%) a reasonable reading
given the divisions of the xaxis in increments of 1%
effectively?
0 1
2 3 4
5 6
7 8
9 10 11 12 13 14 15 16
67
II) How to Determine the Number of Significant Figures in a Measurement
There are 6 to 7 rules for the identification of significant figures. There are also at least 2 other rules for
manipulating measurements in light of significant figures. You are welcome to memorize the first 6 rules,
they are listed in your text.
Or: I can offer you an alternative that has you memorize only 2 rules instead of the first 6. Which would
you prefer to do?
I’LL WAIT … YOU LET ME KNOW WHAT YOU WANT TO DO….
…..YEAH, I THOUGHT SO….
A) Here is a simple fact ...
There are only 2 types of measurements
measurements recorded using
decimal point
161.95 cm
measurements recorded withOUT
a decimal point (often the results of calculation)
3,000 Joules
You can’t assume a decimal point
2,448.000 kJ
260 grams
0.00341 grams
You cannot "just write in" a decimal
point, when one is not given to you or
justified by the sig figs of a calculation.
Directions: We will break into groups of 2 (NOT 3...). When we have an odd number of students, let me know
and I will assign a group of 3 students. Groups should sit where I direct.
Follow my directions carefully. Your task is to answer the three questions at the bottom of the next page. You
will have 7 minutes. STOP. DO NOT go on to the next page ...
You are about to engage in a little inductive reasoning ...
This is a form of thinking that really uses analysis. Inductive reasoning utilizes an initial observation of data,
which can lead to the elucidation of a certain pattern(s). This recognition of pattern(s) [or lack of pattern(s)]
allows us to make tentative predictions that may lead to a general theory about how something works, or the
rules by which something works.
These predictions are then tested by designing specific experiments to test hypotheses and the results, via
deductive thinking (related terms: deduction, deduce ...) are analyzed ... and this too is all about analysis!!!!
But for now ... here is the work of a marvelous educator ... Hilda Taba, and an opportunity to become more
aware of how you can approach a problem with some of the tenets of the Taba Inductive Model of Thinking.
68
RULES FOR SIG FIGS: MEASUREMENTS WITH A DECIMAL POINT
DIRECTIONS: Using your analytical abilities and the data, correctly write rules that address the three situations at the bottom.
MEASUREMENTS WITH A
DECIMAL POINT
(assume a units of millimeters)
NUMBER OF SIGNIFICANT
FIGURES IN THE GIVEN
MEASUREMENT
1.894
4
25.0
3
41.9021
6
677.009
6
3.000
4
5.0
2
0.274
3
0.3
1
0.0331
3
8,329.00
6
7.00000
6
0.0061
2
0.00610
3
0.006104
4
0.0061040
5
0.00045000
5
0.2850
4
0.0000000
0
3,452.7
5
0.000009
1
5,010.00
6
1. Given a measurement with a decimal point, when should you start to count the number of significant figures?
_______________________________________________________________________________________________
2. Write a rule which identifies when any integer, 1-9, is considered to be a SIGNIFICANT FIGURE in a
measurement with a decimal point. _________________________________________________________________
3. Given a measurement that has a decimal point, write ONE rule about the significance of a zero. _________________
__________________________________________________________________________________________________
69
RULES FOR SIG FIGS: MEASUREMENTS WITHOUT A DECIMAL POINT
DIRECTIONS: Using your analytical abilities and the following data, correctly write rules that address the three
situations found at the bottom of this page.
MEASUREMENTS WITHOUT A
DECIMAL POINT
(assume all units are in millimeters)
NUMBER OF SIGNIFICANT FIGURES
IN THE MEASUREMENT
82
2
1998
4
101
3
1001
4
10,010
4
100
1
345
3
70
1
2,507
4
2,390
3
2,001
4
60,000
1
_
60,000
_
60,000
_
60,000
_
60,000
4
2
5
3
11,233
5
88,000
2
1. Write a rule that summarizes when any 1-9 integer is a SIGNIFICANT FIGURE in a measurement with no
decimal point. ______________________________________________________________________________
_
2. Write a rule regarding the role of the dash over a zero ( 0 ) in a measurement with no decimal point. _____________
______________________________________________________________________________________________
3. There are a number of rules that govern the "significance of a zero". Write two separate rules that explain
when zeros are or are not significant in a measurement without a decimal point. ___________________________
_______________________________________________________________________________________________
________________________________________________________________________________________________
70
PRACTICE: IDENTIFYING THE NUMBER OF SIG. FIGS.
DIRECTIONS: Complete the following mind map of "sig fig" rules. Once done, use the mind map to answer each question in the
practice section.
Rules for Determining The Number of Sig Figs
There are two types
of measurement
One type of measurement
The second type of measurement
* has a decimal point recorded
* does NOT have a decimal point recorded
The overall rule is:
The overall rule is
When the measurement has a * decimal point
When the measurement does NOT * have a decimal point
then significant figures begin with the first
then significant figures begin with the first
* 1 to 9
* 1 to 9
integer and includes all other digits
_
(even 0) except for any FINAL zeros
integer and includes all of the
other digits, even tailing zeros
Practice : Underline or circle all of significant figures in each of the following measurements.
a) 10,000 meters
b) 0.0247 Liters
c) 1,806 torr
d) 2007 Å
e) 150.00 kilograms
f) 150 kilograms
_
g) 150 kilograms
h) 150. kilograms
i) 1800 m2
j) 44.000 grams
k) 1,920 Liters
l) 35,000 kg
m) 3400.0 mL
n) 456.90 kPa
_
o) 20 feet
p) 40. mg
q) 0.000340 grams
r) 0.02005 Liters
s) 100.022 moles
t) 50.600 grams
u) 0.707 kPa
v) 0.7070 kPa
w) 0.0070700 kPa
x) 0.2 kPa
y) 4000 kg
_
z) 7,300 meters
*TN: ACTIVITY: How can I determine the number of sig figs a measurement has? Combine the above 2 rules
into a single rule, you would be willing to memorize.
71
III) Calculating and getting a “right answer” with significant figures in mind
A) Exact Numbers (or absolute numbers) and Significant Figures
1) exact (absolute) number = *any counted number (e.g. 2 persons, 3 reasons)
* or a defined value that doesn’t vary (e.g. 1 ft = 12 inches)
2) exact or absolute numbers are NOT used when determining the number of sig figs in a
calculated answer, as a rule.
B) Significant Figures and Scientific Notation
1) Only the integers of the base numbers are significant
a) 250,000 cm = * 2.5 x 105 cm
c) 56.0 ppm = *5.60 x 101ppm
b) 143 joules = *1.43 x 102 joules
d) 4,300,000 mL = *4.3 x 106 mL
C) Summary of Rules: The # of sig figs in your answer is very, very dependent upon the arithmetic
operation you’re performing!
Operation
Multiplying &
Dividing
The recorded answer depends upon
* the fewer number of sig. figs.
Rule
* The answer is recorded with the same number of sig
figs as that term with the fewest sig figs.
NB: Absolute (or Exact) numbers are ignored when determining the number of
sig. figs., in an answer. Absolute (or Exact) numbers include, counted items, the
number “1” and at times, a few constants.
Adding &
Subtracting
Mixed
Calculations
the fewer number of decimal
places (not, strictly, the number
of sig. figs…)
*the answer must be written with the same number of
decimal places as that term with the fewest number of
decimal places.
When adding (or subtracting) &
multiplying (or dividing) are
involved.
Follow the order of operations, carrying over a few “guard
digits” from each operation and adjust for sig figs as you
go.
When only like operations are
involved
Carry a few guard digits and adjust for significant figures
at the end.
72
D) How to work with sig figs and your calculator
Rule : When multiplying or dividing the answer must have * the same number of sig figs
as the measurement in the problem having the * fewest number of sig figs
Reminder: on rounding: Count off the correct number of sig figs, go to the next value and if it is 5 or greater, round the last sig fig up.
Measurements and Operation
(a) (5.229 m) ( 82.7 m)
(b) (0.0322 cm) ( 6.5 cm)
(c)
4.08 g
0.061 cm
(d)
9.475 g
12.05 cm3
Calculator
Answer
0.7863
7
(f)
6.2 grams
3.1 seconds
2
(g)
8.1 kg
.
(4.5 cm) (4.0 cm)
(i)
18 grams
12 Kelvin
*4
*0.7863 g/cm3
*7.863 x 10-1 g/cm3
2.0 m x 3.5 m
(75.0 L) (15 atm)
(2.5 mol) (0.50 K)
Correct answer: with sig figs
and units & THEN in Scientific
Notation
3:This is a multiplication prob.
2
432.4383 and 82.7 being the term with
432 m
the fewest sig. figs., limits the
4.32 x 102 m2
answer to 3 sig figs.
2: This is a multiplication and
0.2093 6.5 is the factor which limits * 0.21 cm2
the answer to only 2 sig figs.
* 2.1 x 10-1 cm2
*2
*67 g/cm
66.885
*6.7 x 101 g/cm
(e)
(h)
Number of sig. figs. the answer
SHOULD have is:
0.45
900
*2
*2
*2
*2
*7.0 m2 or 7.0 x 100 m2
*2.0 g/s or 2.0x 100 g/s
*0.45 kg/cm2
*4.5 x 10-1 kg/cm2
_
*900 L·atm/mol·K
*9.0 x 102 L·atm/mol·K
1.5
(j)
(5.0 cm) (120 cm)
600
(k)
(4.0 ˚C) (5.0 g)
20
(l) (6.00 g) (45˚C) (1.00 J)
g•˚C
270
(m) (10.0 g)(5.0˚C) (1.00 J )
g•˚C
50
*2
*2
*2
*2
*2
*1.5 g/K or 1.5 x 100 g/K
_
*600 cm2 or 6.0 x 102 cm2
_
*20. or 20 or 2.0 x 101˚C·g
*270 J or 2.7 x 102 J
_
*50. J or 50 J or 5.0 x 101 J
73
DIRECTIONS: Complete each of the following questions by providing the best available answer. The correct
answer must have: correct sig figs, correct units, (I have given the answers using scientific notation)
1.
(2.4 x 102 m) (4.321 m) = x
ans. = 1.0 x 103 m2
2.
(109 cm) (36.812 cm) = x
ans.= 4.01 x 103 cm2
3.
14.923 g = x
112.4 mL
4.
(2.3 x 10-3 Joules)
(5.27 x 108 grams)
5.
(4.326 x 108 Joules) = x
(7.91237 x 102 grams)
ans.=1.328 x10-1g/ml
=
x
ans. = 4.4 x 10 –12 J/g
ans.= 5.467 x 105 J/g
For questions 6 –10 identify the number of sig figs that should be in the answer. You don't need to solve the
problem, just write down the number of significant figures in which the answer should be recorded.
____6) (17.00 cm)(2.0 cm)
2
____7) (1,509 torr)(3.81 Liter)
3
____8) 2.00 grams/1.18 milliliter
3
____9) (5.612 x 106m) (8.5 x 109m)
2
___10) 6.880 x 10-2 g / 3.0045 x 10-4mL
4
74
Adding And Subtracting Measurements
Rule : 1) When adding or subtracting the answer must be written with the * same number of decimal places
as the measurement in the problem having the * fewest number of decimal places
PRACTICE:
1) x = 10.000 g + 91.00 g
101.00 g
2) x = (0.0039 g) - (0.00040 g)
0.0035 g
3) x = 27.09g + 2.3g
29.4 g
PUTTING IT ALL TOGETHER
For questions in this section, select from among the choices which describe the validity of the “assertion” and
the validity and relationship of the “reason”.
ASSERTION
1) True
2) True
3) True
4) False
5) False
REASON
True statement and correctly explains or predicts the assertion
True statement, but does NOT correctly explain or predict the assertion
False
True
False
For example:
Assertion
Mr. D. is a chemistry teacher.
because
Reason
Mr. D has brown eyes.
Answer: The best answer is “2”. Even though both statements are true, the reason does not explain nor support the assertion statement.
ASSERTION
REASON
4. The solution to (10.0cm) (15.0 cm)
equals 150 cm2
because
5. The measurement 1220 g has 3
significant figures.
because
6. The sum of 11.000 g + 3.0 g is
correctly written as 14.0 g
because
When multiplying, an answer must have the same
number of significant figures as that term with the
fewest significant figures.
Integers (1- 9) are significant, and final zeros in
measurements without decimals points are not
significant.
When adding, the sum must be expressed in the
same number of decimal places as that original
term with the fewest decimal places.
Answers
4. 4
5. 1
6. 1
75
NAME _______________________________________
SIG FIGS. PRACTICE 1
DIRECTIONS : Questions 1-5 deal with addition and subtraction exclusively. Recall that the rule for addition and
subtraction is a DIFFERENT rule from that of multiplication and division. DO NOT re-write your answer(s) in
scientific notation – BUT be sure each answer has a correct unit (including each value in #5)!
1. solve:
(45.68 cm) + (5.0 cm ) = x
answer __________________
2. solve:
(88.300 g) - (18.20 g) = x
answer __________________
3 solve: (34 cm ) + (5.00 cm) = x
answer _________________
4. Water with a mass of 35.4 g, is added to an empty Erlenmeyer flask with a mass of 87.432 g. The mass of
the flask and water is 146.72 g after a rubber stopper is added. Express the mass of the stopper in grams.
answer = _________________
5. Below is a data table regarding the production of the compound magnesium oxide. The following expresses
the reaction:
2 Mg(s) + O2(g)  2 MgO(s) + 1.202 x 103 kJ
Your job is to complete the table, using the provided data and the rules for adding &/or subtracting
measurements.
Mass of empty crucible and top
19.384 grams
Mass of crucible, top , and magnesium
19.483 grams
Mass of just magnesium
Mass of crucible, top and magnesium oxide
19.547 grams
Mass of magnesium oxide
Mass of oxygen reacted
(hint: Think about applying MR # 1)
76
DIRECTIONS: Use the equations for density and percent error, found on Table T of your reference charts to
complete question 6 and 7. Be sure that you use correct sig figs or the correct number of decimal places!!! I
have provided, as well, the means by which you are to solve most equation based problems. The process is
known as E.S.A. (equation, substitution, answer). The "equation" is the word form of the equation you use.
Substitution is the point at which you replace the words with measurements. The "answer" must have a
correct unit and be in correct sig. figs.
6. A student estimated the volume of a liquid in a beaker as 200 mL. When she poured the liquid into a
graduated cylinder, she measured the volume as 208.0 mL. Assuming the graduated cylinder volume as
the accepted value, calculate the per cent error. The equation for per cent error is on Table T. (Recall that a positive
or negative value for per cent error is just a reflection of the measured value being greater than or less than the accepted value. A + value means your value is
greater than accepted, and a – value indicates your measurement is less than the accepted )
Equation:
Substitution :
Answer _______________
7. The density of pure gold is 19.3 g/cm3. A bright, gold-colored bar of metal massing 57.3 g has a volume of 4.70 cm3.
Calculate the bar's density and then answer yes or no as to whether the bar is pure gold.
Equation :
Substitution:
Answer ____________ and _______________
77
DIRECTIONS : Using the rules for rounding a measurement, sig figs and scientific notation, answer questions
8-14 correctly. Recall that only the base number is important for sig figs when dealing with scientific notation.
___ 8. How many sig figs are in the following measurement?
8.102 x 103 Liters
___ 9. How many sig figs are in the following measurement?
7.00 x 101 grams
___ 10 How many sig figs are in the following measurement?
2.3 x 10-4 Joules
For questions 11-14) round each value to only 3 sig figs
11
903.2 meters = _________________
12
903.8 meters = _________________
13
2,039 meters = _________________
(query: is the magnitude correct?)
14
40,809 meters = _________________
(query: is the magnitude correct?)

Directions: Complete the following. 15-20 each
have only a SINGLE CORRECT answer.
_____15) (6.000 x 10 -4 cm) (4.2 x 102 cm) = x
1)
2)
3)
4)
2.52 x 10 -1 cm2
2.5 x 10-1 cm2
0.252 x 10-2 cm2
2.5 x 10-2 cm2
1) 118.0 ˚C
2) 120 ˚C
3) 118 ˚C
4) 120. ˚C
_____ 19) (50.5 g) (37.981 Joules/g) = x
_____16) 88.021 g / 4196 mL =x
1) 2.09774 x 10-2 g/mL
2) 2.09774 x 10-3 g/mL
3) 2 x 10-2 g/mL
4) 2.098 x 10-2 g/mL
_____17) 5.671cm + 7.99101cm + 8.2 cm = x
1) 21.9 cm
2) 21.86201 cm
_____ 18) 391 K = ˚C + 273
1)
2)
3)
4)
1918 Joules
19 Joules
1920 Joules
192 Joules
_____ 20) x =(6.921 x 10-1 m) (8.0234 x 10-2 m)
1) 5.553 x 10-2 m2
2) 5.6 x 10-2 m2
3) 5.553 x 10-3 m2
4) 5.6 x 10-3 m2
3) 22 cm
4) 21.86 cm

78
For questions 21-25 one or more of the responses given
are correct. Decide which of the responses is (are)
correct. Evaluate each choice carefully, then choose :
1)
2)
3)
4)
5)
when only I is correct
when only II is correct
when only I and II are correct
when only II and III are correct
when I, II, and III are correct
____21) The acceptable solution to
(10.9 cm) (48.805 cm) = x
I) must have only 3 sig figs in the answer,
due to the rule for multiplication/division
_____25) The acceptable solution to
(407.922g)  (12.750 g) = x
I) equals 395.172 grams
II) must have the same number of decimal
places as the term with the fewest
decimal places
III) may have only three decimal places
26. A plot of land has been measured and those
values are recorded as in the representative diagram.
II) equals 5.32 x 102 cm2, using scientific
notation
III) should be written as 531.9745 cm2
_____22 ) The most correct answer to
(89.371mL) + (2.01mL) + (9.1mL) + (16.70mL) = x
I)
must have 2 sig figs.
II) is 117.2 ml
III) may have only 1 decimal place
_____23) The most correct solution to
5.7 x 10-6J = x
1.27 x 101g
I) will have 2 sig figs
II) equals 4.5 x 10-7 J/g,
using scientific notation
6 meters
7.0 meters
Do you note the difference in measurement technique?
a) Calculate the area of the plot. Express the
answer with the correct number of significant
figures.
b) Calculate the perimeter of the plot. Express the
answer with the greatest possible precision.
27) What is the purpose/advantage to reading a
measuring tool and then estimating another place?
III) equals 0.00000045 J/g when taken
out of scientific notation
_____24) The acceptable solution to 23.023 g = x
312.1 mL
I) should be written as 0.073768 g/mL
II) must have only four sig figs
III) equals 7.377 x 10-2 g/mL
28) Which of these is NOT a means of indicating
accuracy?
1) taking a square root
2) providing a range
3) averaging
4) finding percent error
79
Answers:
1. 50.7 cm The operation is addition, therefore, your answer must have the same number of DECIMAL PLACES as the term
with the fewest decimal places. In this case, 5.0 cm has only 1 decimal place, so your answer may have only
1 decimal place.
45.68
5.0
50.68
is your calculator answer.
Count off 1 decimal place, stop the number, and see if you need to round.
50.6| 8 You MUST round. So, the answer is 50.7 cm
2. 70.10 g
The operation is subtraction, therefore, your answer must reflect the same number of DECIMAL PLACES as the factor
with the fewest decimal places. This one is trickier however ! The fewest number of decimal places is 2 ( from the
18.20 g) . When you do your subtraction on your calculator, your calculator only gives you 70.1 You must WRITE
IN THE EXTRA 0, in order to meet the rule's requirement for decimal places
Your calculator says 70.1
But you need 2 decimal places according to the rule so you
must re-write your calculator's answer as 70.10 g SO YOU MUST PROVIDE an extra 0 !!!!
3. 39 cm
The measurement of 34 cm is the limiting measurement, because it has NO DECIMAL PLACES, therefore, your answer
must have NO DECIMAL PLACES.
4. 23.9 grams
6) 4%
7) 12.2 g/cm3 and no it is not pure gold
8) 4
9) 3
10) 2
11) 903 m
12) 904 m
13) 2,040 m (the "non-significant" 0 is needed to keep the number in the thousands: the 0 is for magnitude)
14) 40,800 m (the last two 0's are NOT significant figures - but are needed to keep the value in the ten thousands
15) 2 rule: multiplication, fewest sig figs so, Calculator = 25.2 x 10 -2
use teeter totter, then adjust for sig figs (only 2)
Rewrite = 2.5 x 10-1
16. 4 rule: division, fewest sig figs so, Calculator = 0.0209774 Rewrite = 2.09774 x 10-2 use teeter totter,
then adjust for sig figs (only 4)
17. 1 rule : addition, fewest decimal places (which in this case is only 1)
18. 3 rule : subtraction, fewest decimal places (which in this case is 0)
19. 3 rule : multiplication, fewest sig figs so, Calculator = 1918.0405
1,91 | 8
adjust for sig figs (only 3) and you will note the need to round:
becomes 1,920 (the final zero is for magnitude only)
20. 1 rule: multiplication, fewest sig figs
21. 3 rule: multiplication, fewest sig figs 22. 4 rule: addition, fewest decimal places
23. 5 rule: division, fewest sig figs
24. 4 rule: division, fewest sig figs
25. 5
26. The area is 40 m2 . Because of the poor measurement of the width (6 meters has only 1 sig fig) the product of
(6 meters) (7.0 meters) may be expressed with only 1 significant figure.
Thus, your calculator’s answer of 42 becomes 40 (with the non-significant 0 put in the answer to maintain
the proper magnitude (or relative size) of the answer.
The perimeter is 26 meters Again, 26.0 meters would be inappropriate as an answer, because the less precise measurement of
6 meters limits the number of DECIMAL places the answer can have. Recall the rule that when adding, sig figs take a back seat
and the answer must have the same number of decimal places as the measurement with the fewest.
27) Even though some error is introduced by estimating to the next place, the scientist can better express the reality of the
measurement. S/he helps to increase the number of significant figures of the measurement by such an estimation and thereby
actually helps to reduce the error, once calculations are done with the value(s), based upon the rules.
28) 1
80