Download Study Guide for Skills Module 2—Review of Rounding Rules

Chemistry 1020, Skills Module 2-Rounding
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Study Guide for Skills Module 2—Review of Rounding Rules
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Reading Assignment:
The reference manual which came with your calculator (if needed).
Guide for Your Lecturer:
✔
✔
✔
✔
✔
✔
1.
2.
3.
4.
5.
6.
Quick Review of Algebraic Manipulation
The Calculator: Raising a Number to a Power or Obtaining the Root of a Number
Rounding Rules for Multiplication and Division (Review from Module 1)
Rounding Rules for Addition and Subtraction (Review from Module 1)
Rounding Rules When Taking Logs or Antilogs (Review from Chem 1020 Skills Module 1-Logs)
Practice Using All of the Rounding Rules
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Homework
Note: ✔ indicates problems to be stressed on drill quizzes and hour exams.
✔✔✔■Quick Review of Algebraic Manipulation
1a) S. Given 0.612m/(4.1n + 2.1m) = 0.42, solve for m.
0.612m/(4.1n + 2.1 m) = 0.42
Starting Equation
0.612m = 0.42(4.1n + 2.1 m)
Obtained by multiplying both sides by (4.1n + 2.1 m)
0.612m = 1.72n + 0.882m
Obtained by multiplying through by “0.42”
0.612m - 0.882m = 1.72n
Obtained by subtracting "0.882m" from both sides
So -0.27m = 1.72n
which can be reduced to m = 6.4n
----------------------------------------------------------------------------------------------------------------------------------------------A. Given 1.24n /(4.23n + 1.37m) = 1.25, solve for n.
----------------------------------------------------------------------------------------------------------------------------------------------B. Given 1.9n /(2.5n + 3.9m) = 1.48, solve for m.
----------------------------------------------------------------------------------------------------------------------------------------------C. Given 2.05r /(4.93r + 3.72m) = 0.308, solve for r.
----------------------------------------------------------------------------------------------------------------------------------------------D. Given 2.9r/(4.34r + 2.3m) = 7.89, solve for m.
----------------------------------------------------------------------------------------------------------------------------------------------E. Given 9.7n/(6.5n + 4.2m) = 0.521, solve for m.
-----------------------------------------------------------------------------------------------------------------------------------------------
Xavier University of Louisiana
73
Chemistry 1020, Skills Module 2
✔✔✔■Quick Review of Algebraic Manipulation (continued)
1a) F. Given 4.5n/(6.7n + 7.6m) = 9.6, solve for n.
----------------------------------------------------------------------------------------------------------------------------------------------G. Given 1.20r/(6.88x + 4.78r) = 8.21, solve for r.
----------------------------------------------------------------------------------------------------------------------------------------------H. Given 0.65r/(3.6x + 4.8r) = 8.3, solve for x.
----------------------------------------------------------------------------------------------------------------------------------------------b) A. Given 2.1x /(2.05n - 8.3x) = 4.62, solve for x.
----------------------------------------------------------------------------------------------------------------------------------------------B. Given 9.70x /(5.60n - 0.11x) = 7.8, solve for n.
----------------------------------------------------------------------------------------------------------------------------------------------C. Given 2.7r /(3.4r - 6.1m) = 9.8, solve for r..
----------------------------------------------------------------------------------------------------------------------------------------------D. Given 9.88r /(1.20r - 3.43m) = 4.03, solve for m.
----------------------------------------------------------------------------------------------------------------------------------------------E. Given 7.8m/(4.1n - 9.1m) = 1.11, solve for m.
----------------------------------------------------------------------------------------------------------------------------------------------F. Given 3.15m/(2.44n - 3.97m) = 2.30, solve for n.
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74
Xavier University of Louisiana
Chemistry 1020, Skills Module 2-Rounding
Name
✔✔✔■Quick Review of Algebraic Manipulation (continued)
1b) G. Given 3.10r/(2.92r - 0.314x) = 2.81, solve for r.
----------------------------------------------------------------------------------------------------------------------------------------------H. Given 3.9r/(5.2r - 4.3x) = 9.7, solve for r.
----------------------------------------------------------------------------------------------------------------------------------------------✔✔✔■The Calculator: Raising a Number to a Power or Obtaining the Root of Number
2a) Determine the value of x in the given expression and then round off using the rules above.
R
S. x = (2.1)5(1.8)7/(6.3)4 = 1.587003231 = 1.6
--------------------------------------------------------------------------------------------------------------------------------------------A. x = (6.9)4(1.05)5/(7.1)3
--------------------------------------------------------------------------------------------------------------------------------------------B. x = (1.72)8(4.32)4/(6.82)6
--------------------------------------------------------------------------------------------------------------------------------------------C. x = (5.23)7(1.01)3/(2.1)4
--------------------------------------------------------------------------------------------------------------------------------------------D. x = (1.09)6/(6.4)4*(7.3)5
--------------------------------------------------------------------------------------------------------------------------------------------E. x = (2.9)5/(1.4)3*(9.3)4
--------------------------------------------------------------------------------------------------------------------------------------------F. x = (6.5)5(2.7)3/(3.7)4
--------------------------------------------------------------------------------------------------------------------------------------------G. x = (4.9)6/(3.5)4*(7.2)8
--------------------------------------------------------------------------------------------------------------------------------------------H. x = (7.6)3(8.9)4/(2.6)6
---------------------------------------------------------------------------------------------------------------------------------------------
Xavier University of Louisiana
75
Chemistry 1020, Skills Module 2
✔✔✔■The Calculator: Raising a Number to a Power or Obtaining the Root of Number
(continued)
2b) Determine the value of x in the given expression and then round off using the rules above.
R
S. x4 = (4.2)(3.15)/(17.1) = 0.937866305 = 0.94
--------------------------------------------------------------------------------------------------------------------------------------------A. x3 = (6.9)(1.05)/(7.1)
--------------------------------------------------------------------------------------------------------------------------------------------B. x6 = (1.72)(4.32)/(6.82)
--------------------------------------------------------------------------------------------------------------------------------------------C. x5 = (5.23)(1.01)/(2.1)
--------------------------------------------------------------------------------------------------------------------------------------------D. x5 = (1.09)/{(6.4)*(7.3)}
--------------------------------------------------------------------------------------------------------------------------------------------E. x4 = (2.9)/{(1.4)*(9.3)}
--------------------------------------------------------------------------------------------------------------------------------------------F. x3 = (6.5)(2.7)/(3.7)
--------------------------------------------------------------------------------------------------------------------------------------------G. x6 = (9.1)/{(2.5)*(8.2)}
--------------------------------------------------------------------------------------------------------------------------------------------H. x7 = (5.7)(4.3)/(4.8)
--------------------------------------------------------------------------------------------------------------------------------------------✔✔✔■Rounding Rules for Multiplication and Division (Review from Module 1)
3. How to Round Off
a) State the rules for rounding off numbers. (If the portion to be dropped is greater than or equal to five, round up.
If it is less than five, leave it alone.)
b) Round off one digit from each of the following numbers using the rules above.
|Number
| Number rounded off
||Number
| Number rounded off
|
S. | 0.0075
|
0.008
|| 8745
8750 or 8.75*10 3
|
|
||
|
|
| 0.00172
|
0.0017
|| 308*10-5
3.1*10 -3
|
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||
|
|
A. | 0.00325
|
|| 786
|
|
||
|
|
| 0.00217
|
|| 239*10-3
|
|
||
|
|
B. | 0.0256
|
|| 4732
|
|
||
|
76
Xavier University of Louisiana
Chemistry 1020, Skills Module 2-Rounding
Name
✔✔✔■Rounding Rules for Multiplication and Division (Review from Module 1)
3b) Round off one digit from each of the following numbers using the rules above.
|Number
| Number rounded off
||Number
| Number rounded off
|
| 0.0475
|
|| 489*10-4
|
|
||
|
|
C. | 0.02765
|
|| 4435
|
|
||
|
-1
|
| 0.00198
|
|| 412*10
|
|
||
|
c) Uncertainty: Significant Digits
It is important that we indicate the uncertainty in measured numbers. One way of doing so is to count the
number of significant digits. Define significant digits.
d)
It is easy to determine the number of significant digits in a number which has only nonzero digits because, by
convention, all nonzero digits in a number are always significant. When a number contains zero’s, however, it
is not quite so easy because zero’s may or may not be significant depending on their placement in the number.
There are three rules for determining whether or not zeros in a number are signficant. State them (pp. 13).
Rule 1: Zero’s to the left of nonzero digits
Rule 2: Zero’s between nonzero digits
Rule 3: Zero’s to the right of nonzero digits
e)
f)
Indicate the number of significant figures in each of the following numbers
|Number
| Number of significant figures
||Number
| Number of significant figures
S. | 0.0075
|
2
|| 8745
|
4
-5
|
| 0.00172
|
3
|| 308*10
3
A. | 0.0000325
|
|| 7.90
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| 0.027
|
|| 239*10-3
|
B. | 0.0206
|
|| 4732
|
-4
| 0.000045
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|| 489*10
|
C. | 0.000005
|
|| 4.04
|
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| 0.00098
|
|| 42*10-1
D. | 10.0
|
|| 213
|
-2
| 200
|
|| 3.05*10
|
Determining the uncertainty in numbers obtained by multiplying or dividing
State the rule used to determine the uncertainty in answers obtained by multiplying or dividing measurements (The
number of significant figures in the result is the same as the number in the least precise measurement in the
calculation.)
Xavier University of Louisiana
77
Chemistry 1020, Skills Module 2
✔✔✔■Rounding Rules for Multiplication and Division (Review from Module 1, continued)
3g) Indicate the number of significant digits in each of the given numbers and then use this information to round
off the result obtained by multiplying the two or dividing one by the other. (p. 15)
|Number
|Significant Figures in Number
||Number
|Significant Figures in Number
-1
|
S. | 0.00541
|
3
|| 9.1*10
2
|
|
||
|
Multiply the two numbers above and round off using the rule in e.
R
-1
(0.00541)*(9.1*10 ) = 0.0049231 = 0.0049 = 4.9*10-3
|Number
|Significant Figures in Number
||Number
A. | 0.0023
|
|| 8.23*10 2
|
|
||
Multiply the two numbers above and round off using the rule in e.
|Significant Figures in Number
|
|
|
B. | 8.02
|
|| 1.2*10 2
|
|
||
|
Divide the first of the two numbers above by the second and round off using the rule in e.
|Number
|Significant Figures in Number
||Number
C. | 8.020
|
|| 5.81*10 2
|
|
||
Multiply the two numbers above and round off using the rule in e.
|Significant Figures in Number
|
|
|Number
|Significant Figures in Number
||Number
|Significant Figures in Number
D. | 0.0072
|
|| 9.346*10 2 |
|
|
||
|
Divide the first of the two numbers above by the second and round off using the rule in e.
|Number
|Significant Figures in Number
||Number
|Significant Figures in Number
|
E. | 0.0732
|
|| 4.3*10 -4
|
|
||
|
Divide the first of the two numbers above by the second and round off using the rule in e.
|Number
|Significant Figures in Number
||Number
|Significant Figures in Number
|
F. | 0.123
|
|| 4.33*10 3
|
|
||
|
Divide the first of the two numbers above by the second and round off using the rule in e.
78
Xavier University of Louisiana
Chemistry 1020, Skills Module 2-Rounding
Name
✔✔✔■Rounding Rules for Addition and Subtraction (Review from Module 1)
4. Determining the uncertainty in numbers obtained by adding or subtracting
a) State the rule used to determine the uncertainty in answers obtained by adding or subtracting measurements (p. 15)
b) Indicate the absolute uncertainty in each of the given numbers and then use this information to round
off the result obtained by adding the two or subtracting one from the other. (p. 14)
|Number
|Absolute Uncertainty in Number ||Number
|Absolute Uncertainty in Number
|
S. | 0.00541
|
±0.00001
|| 0.0023
±0.0001
|
|
||
|
Add the two numbers above and round off using the rule in g.
R
0.00541 + 0.0023 = 0.00771 = 0.0077 = 7.7*10-3
|Number
|Absolute Uncertainty in Number ||Number
|Absolute Uncertainty in Number
|
A. | 0.0023
|
|| 0.822
|
|
||
|
Subtract the first of the two numbers above from the second and round off using the rule in g.
|Number
|Absolute Uncertainty in Number ||Number
B. | 8.02
|
|| 121
|
|
||
Add the two numbers above and round off using the rule in g.
|Absolute Uncertainty in Number
|
|
|Number
|Absolute Uncertainty in Number ||Number
C. | 3.020
|
|| 0.23
|
|
||
Add the two numbers above and round off using the rule in g.
|Absolute Uncertainty in Number
|
|
|Number
|Absolute Uncertainty in Number ||Number
|Absolute Uncertainty in Number
|
D. | 0.0072
|
|| 0.09333
|
|
||
|
Subtract the first of the two numbers above from the second and round off using the rule in g.
|Number
|Absolute Uncertainty in Number ||Number
E. | 0.0732
|
|| 0.0043
|
|
||
Add the two numbers above and round off using the rule in g.
|Absolute Uncertainty in Number
|
|
|Number
|Absolute Uncertainty in Number ||Number
|Absolute Uncertainty in Number
|
F. | 0.123
|
|| 4.3
|
|
||
|
Subtract the first of the two numbers above from the second and round off using the rule in g.
Xavier University of Louisiana
79
Chemistry 1020, Skills Module 2
✔✔✔■Rounding Rules When Taking Logs or Antilogs (Review from Chem 1020 Skills
Module 1-Logs)
5a) How is the uncertainty in “x” related to the uncertainty in “log x?” (The number of digits after the decimal
point in a common log is equal to the number of significant figure in the orignal number. See A5 in the
text.)
b) What are the logarithms of the following numbers?____________
S. •log (1.2*10 -13) = -12.92
•ln (4.81*10 2) = 6.186
c)
80
•log(6.444*10 -7) = -6.1908
A. •log (1.9*10 -11) =
•log (3.43*10 -8) =
•ln (9.00*10 6) =
B. •ln (6.51*10 -4) =
•ln (2*10 2) =
•log (9.2*10 -1) =
C. •log (9.83*10 3) =
•ln (8.02*10 -7) =
•log (8.8*10 17) =
D. •ln (1.89*10 -3) =
•log (1.12*10 3) =
•ln (7*10 27) =
E. •log (4.2*10 -6) =
•log (8.233*10 4) =
•ln (1.92*10 19) =
What are the antilogarithms of the following numbers?____________
S. •104.12 = 1.3*10 4
•e3.113 = 2.25*10 1
•10-6.4123 = 3.870*10 -7
A. •101.911 =
•e-3.43 =
•109.0 =
B. •e-6.514 =
•102.1 =
•e-9.223 =
C. •109.833 =
•e-8.027 =
•10-8.87 =
D. •e1.893 =
•1011.2 =
•e-4.94 =
E. •105.87 =
•e9.2122 =
•10-9.234 =
Xavier University of Louisiana
Chemistry 1020, Skills Module 2-Rounding
Name
✔✔✔■Practice Using All of the Rounding Rules
6. Determine the answer after each step in the following algorithm using the rounding rules above and carrying one
extra digit until you get to the final answer.
S.
Step 1: Add 2.31 to 1.8213
Answer to step 1: __4.121*__________
(*one extra digit kept)
Step 2: Multiply the result from step 1 by 8.2314*102
Answer to step 2: __3.392*10 3 *______
Step 3: Take the log of the result from step 2
Final answer:
__3.531___________
-----------------------------------------------------------------------------------------------------------------------------------------------------A.
Step 1: Multiply 2.31*103 by 4.12*10-3
Answer to step 1: ___________________
Step 2: Subtract the result from step 1 from 9.731
Answer to step 2:
___________________
Step 3: Take the ln of the result from step 2
Final answer:
___________________
-----------------------------------------------------------------------------------------------------------------------------------------------------B.
Step 1: Take the log of 6.21*10-6
Answer to step 1: ___________________
Step 2: Multiply the result from step 1 by 8.2*10-1
Answer to step 2: ___________________
Step 3: Add 3.124 to the result from step 2
Final answer:
___________________
-----------------------------------------------------------------------------------------------------------------------------------------------------C.
Step 1: Subtract 152.034 from 212.3
Answer to step 1: ___________________
Step 2: Multiply the result from step 1 by 3.11*10-2
Answer to step 2:
___________________
Step 3: Take the antilog of the result from step 2
Final answer:
___________________
-----------------------------------------------------------------------------------------------------------------------------------------------------D.
Step 1: Take the inverse ln of 2.682
Answer to step 1: ___________________
Step 2: Divide the result from step 1 by 2.1*10-1
Answer to step 2:
___________________
Step 3: Add 14.11 to the result from step 2
Final answer:
___________________
-----------------------------------------------------------------------------------------------------------------------------------------------------E.
Step 1: Subtract 14.211 from 153.1
Answer to step 1: ___________________
Step 2: Divide the result from step 1 by 6.23*102
Answer to step 2: ___________________
Step 3: Take the antilog of the result from step 2
Final answer:
___________________
-----------------------------------------------------------------------------------------------------------------------------------------------------F.
Step 1: Add 0.012 to 0.368
Answer to step 1: ___________________
Step 2: Multiply the result from step 1 by 3.21*101
Answer to step 2:
___________________
Step 3: Take the inverse ln of the result from step 2
Final answer:
___________________
------------------------------------------------------------------------------------------------------------------------------------------------------
Xavier University of Louisiana
81
Chemistry 1020, Skills Module 2
✔✔✔■Practice Using All of the Rounding Rules (continued)
6. Determine the answer after each step in the following algorithm using the rounding rules above and carrying one
extra digit until you get to the final answer.
G.
Step 1: Take the inverse ln of 3.681
Answer to step 1: ___________________
Step 2: Multiply the result from step 1 by 1.12*10-2
Answer to step 2:
___________________
Step 3: Add 10.1 to the result from step 2
Final answer:
___________________
-----------------------------------------------------------------------------------------------------------------------------------------------------H.
Step 1: Divide 16.21 into 101
Answer to step 1: ___________________
Step 2: Add 0.21 to the result from step 1
Answer to step 2: ___________________
Step 3: Take the antilog of the result from step 2
Final answer:
___________________
-----------------------------------------------------------------------------------------------------------------------------------------------------I.
Step 1: Divide 17.22 by 1.21*103
Answer to step 1: ___________________
Step 2: Add the result of step 1 to 1.62
Answer to step 2: ___________________
Step 3: Take the inverse ln of the result from step 2
Final answer:
___________________
-----------------------------------------------------------------------------------------------------------------------------------------------------J.
Step 1: Take the antilog of -2.11
Answer to step 1: ___________________
Step 2: Multiply the result from step 1 by 4.36*102
Answer to step 2:
___________________
Step 3: Add 14 to the result to step 2
Final answer:
___________________
-----------------------------------------------------------------------------------------------------------------------------------------------------K.
Step 1: Subtract 8.121 from 8.08
Answer to step 1: ___________________
Step 2: Divide the result from step 1 by 2.18
Answer to step 2:
___________________
Step 3: Take the antilog of the result from step 2
Final answer:
___________________
-----------------------------------------------------------------------------------------------------------------------------------------------------L.
Step 1: Subtract 1.8213 from 2.31
Answer to step 1: ___________________
Step 2: Multiply the result from step 1 by 8.248*10-3
Answer to step 2:
___________________
Step 3: Take the log of the result from step 2
Final answer:
___________________
-----------------------------------------------------------------------------------------------------------------------------------------------------M.
Step 1: Divide 3.21*103 by 4.121*103
Answer to step 1: ___________________
Step 2: Subtract the result from step 1 from 14.2
Answer to step 2:
___________________
Step 3: Take the ln of the result from step 2
Final answer:
___________________
-----------------------------------------------------------------------------------------------------------------------------------------------------N.
Step 1: Take the log of 4.21*10-5
Answer to step 1: ___________________
Step 2: Multiply the result from step 1 by 8.2*103
Answer to step 2:
___________________
Step 3: Add 2.361*103 to the result from step 2
Final answer:
___________________
------------------------------------------------------------------------------------------------------------------------------------------------------
Generated by JWC in Spring, 2000; Revised 2002 & 2003 SJB
82
Xavier University of Louisiana