Scientific Measurement

1
Chapter 3

• Scientific Measurement

2
Measurements

• Qualitative
• Gives results in a description, nonumerical form

• Quantitative
• Give results in a definite form, usually numbers
  and units

3
Accuracy vs. Precision

• Accuracy - how close a measurement is to the
  accepted value
• Precision - how close a series of measurements
  are to each other

ACCURATE CORRECT PRECISE CONSISTENT
4
Accuracy vs. Precision
5
Percent Error

• Indicates accuracy of a measurement

6
Percent Error

• A student determines the density of a substance
  to be 1.40 g/mL. Find the error if the
  accepted value of the density is 1.36 g/mL.

7
Percent Error

• A technician experimentally determined the
  boiling point of octane to be 124.1ºC. The actual
  boiling point of octane is 125.7ºC. Calculate the
  error and percent error.

Error 1.6ºC Percent error 1.273
8
Significant Figures

• Indicates precision of a measurement.
• Recording Sig Figs
• Sig figs in a measurement include the known
  digits plus a final estimated digit

2.31 cm
9
Significant Figures

• Counting Sig Figs
• All non-zero numbers are sig figs
• Zeros depend on location in number
• LEADING zeros never count ---------0.0025
• EMBEDDED zeros always count---- 10,005
• TRAILING zeros only count if
• there is a point. --------------2,500 2,500.
• The underlined zeros do not count.

10
Significant Figures
Counting Sig Fig Examples
1. 23.50
1. 23.50
4 sig figs
3 sig figs
2. 402
2. 402
3. 5,280
3. 5,280
3 sig figs
2 sig figs
4. 0.080
4. 0.080
11
Rounding

• Need to use rounding to write a calculation
  correctly
• Calculator gives you lots of insignificant
  figures and you must round to the right place
• When rounding, look at the digit after the one
  you can keep
• Greater than or equal to 5, round up
• Less than 5, keep the same

12
Rounding

• Round each measurement to 3 sig figs.
• A. 87.073 meters
• B. 4.3621 meters
• C. 0.01552 meter
• D. 9009 meters
• E. 1.7777 meters
• F. 629.55 meters

87.1meters
4.36 meters
0.0155 meter
9010 meters
1.78 meters
630 meters
13
Scientific Notation

• Round each measurement to the number of
  significant figure shown in parenthesis. Write
  the answers in scientific notation.
• A. 314.721 meters (4)
• B. 0.001775 meter (2)
• C. 64.32 X 10-1 meters (1)
• D. 8792 meters (2)

3.147 X 102
1.8 108
60 X 10-1
8.8 X 103
14
Significant Figures

• Calculating with Sig Figs (cont)
• Add/Subtract - The with the lowest decimal
  value determines the place of the last sig fig in
  the answer.

224 g 130 g 354 g
3.75 mL 4.1 mL 7.85 mL
3.75 mL 4.1 mL 7.85 mL
? 350g
? 7.9 mL
15
Significant Figures

• C. 8.7 g 15.43 g 19 g 43.13 g
• D. 853.2 L 627.443 L 225.757 L
• E. 5.47 m 11m 87.3000 m 103.770m

E. 5.47 11 87.3000 103.770
C. 8.7 15.43 19 43.13
D. 853.2 - 627.443 225.757
225.8
104
43
16
Significant Figures

• Calculating with Sig Figs (cont)
• Exact Numbers do not limit the of sig figs in
  the answer. UNLIMITED SIG FIGS
• Counting numbers 12 students
• Exact conversions 1 m 100 cm
• 1 in any conversion 1 in 2.54 cm

17
Significant Figures

• Calculating with Sig Figs
• Multiply/Divide - The with the fewest sig figs
  determines the of sig figs in the answer.

(13.91g/cm3)(23.3cm3) 324.103g
4 SF
3 SF
324 g
18
Significant Figures
Practice Problems

• 1. (15.30 g) (6.4 mL)

4 SF
2 SF
2.390625 g/mL
? 3700
a. 67 X 55 3685
? 0.30
d. 0.034 X 8.8 0.2992
19
Scientific Notation
65,000 kg ? 6.5 104 kg

• Converting into Sci. Notation
• Move decimal until theres 1 digit to its left.
  Places moved exponent.
• Large (gt1) ? positive exponentSmall (lt1) ?
  negative exponent
• Only include sig figs.

20
Scientific Notation
Practice Problems

• 7. 2,400,000 ?g
• 8. 0.00256 kg
• 9. 7 ? 10-5 km
• 10. 6.2 ? 104 mm

2.4 ? 106 ?g
2.56 ? 10-3 kg
0.00007 km
62,000 mm
21
Scientific Notation

• Convert between scientific notation and regular
  notation without changing the of sig figs
• A. 4.61 X 10-4
• B. 3.69 X 106
• C. 0.000597
• D. 23,000,000
• E. 8.00 X 102

22
Scientific Notation

• Calculating with Sci. Notation

(5.44 107 g) (8.1 104 mol)
Type on your calculator
(5.44 X10
7)
(8.1X10
4)

EE
EE
ENTER
671.6049383
670 g/mol
6.7 102 g/mol