Measurements in Chemistry Scientific notation and Significant Figures.
Chapter 2 Measurements Measured Numbers and Significant Figures.
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Transcript of Chapter 2 Measurements Measured Numbers and Significant Figures.
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. . cm
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?
Solution
. l8. . . . I . . . . I9. . . .I . . . . I10. . cmEstimate 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. . cm
What is the length of the line?
1) 6.0 cm
2) 6.06 cm
3) 6.60 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 objects2 soccer balls
1 watch
4 pizzasObtained from a defined relationship
1 foot = 12 inches
1 meters = 100 cmNot obtained with measuring tools
Learning Check
A. Exact numbers are obtained by
1. measuring
2. counting3. 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.
Rules1. 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
Timberlake lecture plus 18
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
Addition/Subtraction with Sig Figs
• Your answer must have the same number of decimal places as the value with the fewest decimal places28.0 + 23.538 + 25.68 = 77.218
Round so that the answer is 77.2
Timberlake lecture plus 20
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 3) 40.7
Timberlake lecture plus 21
Solution
A. 235.05 + 19.6 + 2.1 =
2) 256.8
B. 58.925 - 18.2 =
3) 40.7
Timberlake lecture plus 22
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.
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
Timberlake lecture plus 24
Learning Check
A. 2.19 X 4.2 = 1) 9 2) 9.2 3) 9.198
B. 4.311 ÷ 0.07 = 1) 61.58 2) 62 3) 60
C. 2.54 X 0.0028 =
0.0105 X 0.060
1) 11.3 2) 11 3) 0.041
Timberlake lecture plus 25
Solution
A. 2.19 X 4.2 = 2) 9.2
B. 4.311 ÷ 0.07 = 3) 60
C. 2.54 X 0.0028 = 2) 11 0.0105 X 0.060
Continuous calculator operation =
2.54 x 0.0028 0.0105 0.060