Download Chapter 1 Measurements - Belle Vernon Area School District

Chapter 2
Measurements
Measured Numbers and
Significant Figures
Measured Numbers
When you use a measuring tool is used to
determine a quantity such as your height or
weight, the numbers you obtain are called
measured numbers.
Reading a Meterstick
. l2. . . . I . . . . I3 . . . .I . . . . I4. .
cm
First digit (known)
=2
2.?? cm
Second digit (known)
= 0.7
2.7? cm
Third digit (estimated) between 0.05- 0.07
Length reported
=
2.75 cm
or
2.76 cm
or
2.77 cm
Known + Estimated Digits
 Known digits 2 and 7 are 100% certain
 The third digit 6 is estimated (uncertain)
 In the reported length, all three digits
(2.76 cm) are significant including the
estimated one
Learning Check
. l8. . . . I . . . . I9. . . .I . . . . I10. .
What is the length of the line?
1) 9.2 cm
2) 9.22 cm
3) 9.23 cm
How your answer compare with your
neighbor’s answer? Why or why not?
cm
Solution
. l8. . . . I . . . . I9. . . .I . . . . I10. .
cm
Estimate to the hundreth’s place (0.01 cm)
2) 9.22 cm
3) 9.23 cm
The estimated digit may be slightly different.
Both readings are acceptable.
Learning Check
l5. . . . I . . . . I6. . . .I . . . . I7. .
What is the length of the line?
1) 6.0 cm
2) 6.06 cm
3) 6.60 cm
cm
Solution
l5. . . . I . . . . I6. . . .I . . . . I7. .
cm
Estimate to the hundreth’s place (0.01 cm). The
reading is between 6.0 and 6.1. You may have
estimated 6.07 cm as well.
2) 6.06 cm
Zero as a Measured Number
. l3. . . . I . . . . I4 . . . . I . . . . I5. .
cm
What is the length of the line?
First digit
4.?? cm
Second digit
4.5? cm
Last (estimated) digit is
4.50 cm
(not to the left or right of .5)
Exact Numbers
Obtained when you count objects
2 soccer balls
1 watch
4 pizzas
Obtained from a defined relationship
1 foot = 12 inches
1 meters = 100 cm
Not obtained with measuring tools
Learning Check
A. Exact numbers are obtained by
1. measuring
2. counting
3. definition
B. Measured numbers are obtained by
1. measuring
2. counting
3. definition
Solution
A. Exact numbers are obtained by
2. counting
3. definition
B. Measured numbers are obtained by
1. Using a measuring tool
Learning Check
Classify each of the following as an exact (1)
or a measured (2) number.
A.___Gold melts at 1064°C
B.___1 yard = 3 feet
C.___A red blood cell with diameter 6 x 10-4 cm
D.___There were 6 hats on the shelf
E.___A can of soda contains 355 mL of soda
Solution
Classify each of the following as an exact (1) or a
measured(2) number. Give reason.
A. 2 Requires a thermometer(measuring tool)
B. 1 From a definition in U.S. system
C. 2 Need measuring tool to determine
D. 1 Counted the hats
E. 2 Measured
Significant Figures
• Significant Figures – The digits that
indicate the precision with which a
measurement is made; all digits of a
measured quantity are significant, including
the last digit, which is uncertain.
Sig Fig Inquiry
• Determine the rules for finding the number
of significant digits.
Rules
1. All non-zero numbers are significant.
2. Zeros at the end without a decimal point
are not significant.
3. Zeros at the end with a decimal point are
significant.
4. Zeros in the middle of other numbers are
significant.
5. Zeros at the beginning are NOT significant
Adding and Subtracting
The answer has the same number of decimal
places as the measurement with the fewest
decimal places.
25.2
one decimal place
+ 1.34 two decimal places
26.54
answer 26.5 one decimal place
Timberlake lecture plus
18
Addition/Subtraction with Sig
Figs
• Your answer must have the same number of
decimal places as the value with the fewest
decimal places
28.0 + 23.538 + 25.68 = 77.218
Round so that the answer is 77.2
Learning Check
In each calculation, round the answer to the
correct number of significant figures.
A. 235.05 + 19.6 + 2.1 =
1) 256.75
2) 256.8
3) 257
B.
58.925 - 18.2 =
1) 40.725
2) 40.73
Timberlake lecture plus
3) 40.7
20
Solution
A. 235.05 + 19.6 + 2.1 =
2) 256.8
B.
58.925 - 18.2 =
3) 40.7
Timberlake lecture plus
21
Multiplying and Dividing
Round (or add zeros) to the calculated answer
until you have the same number of significant
figures as the measurement with the fewest
significant figures.
Timberlake lecture plus
22
Multiply/Divide with Sig Figs
• Your answer must have the same number of
sig figs as the measurement with the fewest
number of sig figs.
Calculate the volume if L = 3.65 cm, W = 3.20
cm, and H = 2.05 cm
V = 23.944 cm3, after rounding to the correct
number of sig figs, V=23.9 cm3
Learning Check
A. 2.19 X 4.2 =
1) 9
2) 9.2
B. 4.311 ÷ 0.07 =
1) 61.58
C.
3) 9.198
2) 62
2.54 X 0.0028 =
0.0105 X 0.060
1) 11.3
2) 11
3) 60
3) 0.041
Timberlake lecture plus
24
Solution
A.
2.19 X 4.2
=
2) 9.2
B.
4.311 ÷ 0.07
=
3) 60
C.
2.54 X 0.0028 =
0.0105 X 0.060
2) 11
Continuous calculator operation =
2.54 x 0.0028  0.0105  0.060
Timberlake lecture plus
25