Download Counted or Measured Number?

Module 1: Measurement and Significant Figures
Goal: Use significant figures from measurements to adjust calculated answers.
Chemworks 1
Objectives
a. Distinguish between a
measured number and an
exact number.
Mini-Lecture
Measurement
Standards of Measurement
Tools for Measurement
Exact Numbers
b. Distinguish between
accuracy and precision in
a measurement.
Accuracy
Precision
Pizza Precision
c. Indicate correct number
of significant figures in a
number.
Significant Figures in Measurement
Reading A Meterstick
Known + Estimated Digits
Zero as a Significant Digit
Counting Significant Figures
Leading Zeros
Sandwiched Zeros
Trailing Zeros
d. Report answers to
calculations using the
correct number of
significant figures.
Significant Figures in Calculations
Team Activities
Worksheet M1: Types of
Numbers
Learning Checks
M1
M2
M3
Worksheet M2: M&M’s
Statistics
M4, M5
M6, M7, M8
Worksheet SF1: Counting
Significant Figures
\
SF1
SF2
SF3
SF4
SF5
SF6
Worksheet SF2:Rounding
Numbers
Worksheet SF3:Calculator
Operations
Worksheet SF4:Significant
Figures in Reported Answers
SF7
Types of Numbers
Worksheet M1
A. EXACT NUMBERS
Form a group of 3-4 students and complete the numbers for the following data.
People in your group
People in your group with backpacks
Inches in one foot
Centimeters in one meter
People wearing glasses in your group
Seconds in one minute
1. How were the numbers in part A obtained?
2. Why are each of these numbers called exact numbers?
B. MEASURED NUMBERS
Have each student in your group individually use a meterstick or metric ruler to measure the width (cm)
and the length (cm) of this page of paper. Record the results below.
Width
Length
Student 1
Student 2
Student 3
Student 4
1. How were the numbers in part B obtained?
2. How close were your measurements for width and length?
3. List as many reasons as you can to explain why the measurements for width and length might differ.
M & M’s Statistics
Worksheet M2
Predicted
Number
Actual Number
Counted or Measured Number?
Data
How many M&Ms are in the package?
How many yellow M&Ms?
How many red M&Ms?
How many dark brown M&Ms?
What is the total mass (grams) of
M&Ms listed on the package?
Calculations
% Yellow M&Ms
% Red M&Ms?
% Dark brown M&Ms?
Calories/ M&M
What is the average mass of one M&M
(g/M&M)?
What is the total mass (grams) of all of
the red M&Ms in the package?
Work
Result
Counting Significant Figures
Worksheet SF1
In each of the following example sets, observe the number of significant figures and complete
the blanks. Write a rule for counting significant figures in each set by completing the statement
with the term significant or not significant.
EXAMPLE SET 1
Number of
Significant Figures
38.15 cm
4
5.6 ft
2
65.6 lb
_____
122.55 m
_____
EXAMPLE SET 2
Type of
zeros
Number of
Significant Figures
0.008 mm
leading
1
0.0156 oz
leading
3
0.0042 lb
_________
_____
0.000262 mL _________
_____
EXAMPLE SET 3
Type of
zeros
Number of
Significant Figures
50.8 mm
confined
3
2001 min
confined
4
0.702 lb
_________
_____
0.0405 m
_________
_____
0.008060 g
_________
_____
Type of
zeros
Number of
Significant Figures
25,000 in.
trailing
2
200 yr
trailing
1
48,600 gal
_________
_____
105,000 m
_________
_____
EXAMPLE SET 4
Rule 1:
All nonzero digits are
(significant or not significant)
Rule 2:
Leading zeros (zeros in front of
nonzero digits) are
(significant or not significant)
.
Rule 3:
Sandwiched zeros (zeros between
nonzero digits) are
(significant or not significant)
Rule 4:
Trailing zeros (zeros that follow
nonzero digits) in numbers with no
decimal point are
_____________________
(significant or not significant)
Rounding Numbers
Worksheet SF2
In each problem, observe the number of significant figures, and complete the rules for
determining the number of significant figures in calculated answers from operations of
multiplication, division, addition, and/or subtraction.
ROUNDING OFF NUMBERS OR ADDING PLACEHOLDER ZEROS
Round the following measured numbers to the number of significant figures indicated:
To 3 SFs
To 2 SFs
1.48221
1.48
1.5
0.88822
_________________
_________________
0.0028533
_________________
_________________
508.25
_________________
_________________
386,222
_________________
_________________
3.582 x 105
_________________
_________________
4
4.00
4.0
8
_______________
_________________
RULES FOR ROUNDING
Complete the following to give rules for rounding off.
When the first digit of the numbers to be dropped is less than 5_______________________,
When the first digit of the numbers to be dropped is 5 or greater _____________________,
Complete the following to give rule for adding zeros.
When an answer has fewer significant figures than desired the proper number of significant
figures is acquired by _____________________________________________________
Calculator Operations
Worksheet SF3
Design a sequence to run on the calculator that will solve each of the following
mathematical operations. Carry out the operations to give an answer. Share your
sequence with you neighbors. Make sure that everyone in your group gets the same
answer.
Example:
3.5 x 340 x 0.10 =
x
3.2
x
.10
x 8.5 x 102 =
1.
0.050 x 1.2
2.
6.0 X 10-4
0.15
3.
0.85 x 24
4.8 x 2.5
4.
4.44
5.
55.2 - 24.484
+
15
=
=
0.2
+ 13.254
=
=
=
4.8 (answer)
Significant Figures In Reported Answers
Worksheet SF4
Multiplication and Division
Problem 1:
3.8 in. x 2.54 cm
1 in.
Calculator result
=
Reported Answer
=
0.9652
0.97 cm
How many significant figures are in 3.8 in?
______________________
How many significant figures are in 2.54 cm/in?
______________________
How many significant figures are in the reported answer? ______________________
Explain the reason for the number of significant figures in the reported answer:
Explain how the unit of cm is obtained for the answer.
Problem 2:
100.0 g x 1 mL
2.70 g
Calculator result
x
1 qt
=
946 mL
0.039 15 1202
Reported Answer
=
0.0392 qt
In the setup, show how the units cancel out.
How many significant figures are in 100.0 g?
______________________
How many significant figures are in 2.70 g/mL?
______________________
How many significant figures are in 946 mL/qt?
______________________
How many significant figures are in the reported answer?
______________________
Explain the reason for the number of significant figures in the reported answer:
In setting up a problem, how are the units of the measurements arranged?
Worksheet SF 4 continued
Problem 3:
Reported Answer
Complete the setup and give the reported answer.
1.18 x 1010 in. x
1 sec
2.54 cm
1 in.
x
sec
min
x
min
hr
=
How many significant figures are in 1.18 x 1010 in.?
______________________
How many significant figures are in 2.54 cm?
______________________
Which values are exact numbers?
______________________
Why?
How many significant figures should be in the reported answer?
______________________
Why?
What are the unit(s) of the answer?
______________________
Summarize your method for remembering how to determine the number of significant figures for
reported answers from multiplication and division?
Worksheet SF 4 continued
Addition and Subtraction
Problem 4:
Add: 24.8
Calculator result
+ 1.587 + 24.78
=
51.167
Reported Answer
=
51.2
1. Align the numbers from problem 4 and indicate the number of decimal places in each.
________.____
 ______decimal place(s)
________.____
 ______ decimal place(s)
________.____
 ______ decimal place(s)
2. Which of the added numbers has the fewest decimal places?
___. ________
3. Now carry out the addition:
Sum
________.___
 ______decimal place(s) needed
4. Round off to the correct number of decimal places to find the reported answer:
Reported answer
___________.______
5. How should you determine the final reported answer for addition or subtraction problems?
Problem 5:
Add:
Calculator result
45 + 1.0025
Subtract:
Reported Answer
+ 3.78
______________
_________
41.04 - 34.889
______________
_________
How do you determine the final reported answer for subtraction problems?
Problem 6:
8.26 (2.45 + 5.7)
(0.00452)(856)
=
Which rules will you apply first: rules of addition/subtraction or multiplication/division?