Measurement

1
Measurement

• Accuracy vs Precision
• Percent Error
• Significant Figures
• Scientific Notation
• Temperature Conversions
• Dimensional Analysis
• Conversion Factors
• SI Conversions

2
Number vs. Quantity

• Quantity number unit

UNITS MATTER!!
3
A. 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
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A. Accuracy vs. Precision



5
B. Percent Error

• Indicates accuracy of a measurement

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B. 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.

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C. Significant Figures

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

2.31 cm
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C. Significant Figures

• Counting Sig Figs
• Digits from 1-9 are always significant
• Zeros between two other sig figs are always
  significant
• One or more additional zeros to the right of both
  the decimal place and another sig digit are
  significant
• Count all numbers EXCEPT
• Leading zeros -- 0.0025
• Trailing zeros without a decimal point -- 2,500

739
5085
2.60
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C. 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
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C. 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
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C. 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

3.75 mL 4.1 mL 7.85 mL
3.75 mL 4.1 mL 7.85 mL
? 7.9 mL
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C. Significant Figures

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

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C. Significant Figures
Practice Problems

• 5. (15.30 g) (6.4 mL)

4 SF
2 SF
2.390625 g/mL
6. 18.9 g - 0.84 g
? 18.1 g
18.06 g
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D. Scientific Notation

• A way to express any number as a number between 1
  and 10 (coefficient) multiplied by 10 raised to a
  power (exponent)
• Number of carbon atoms in the Hope diamond
• 460,000,000,000,000,000,000,000 atoms
• 4.6 x 1023 atoms

exponent
coefficient
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D. 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 all of them!

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D. Scientific Notation
Practice Problems

• 7. 2,400,000 ?g
• 8. 0.00256 kg
• 9. 7.0 ? 10-5 km
• 10. 6.2 ? 104 mm

2.4 ? 106 ?g
2.56 ? 10-3 kg
0.000070 km
62,000 mm
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D. Scientific Notation

• Calculating with Sci. Notation

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

671.6049383
670 g/mol
6.7 102 g/mol
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D. Scientific Notation
Practice Problems
4 ? 1010 cm2

• 11. (4 x 102 cm) x (1 x 108cm)
• 12. (2.1 x 10-4kg) x (3.3 x 102 kg)
• 13. (6.25 x 102) (5.5 x 108)
• 14. (8.15 x 104) (4.39 x 101)
• 15. (6.02 x 1023) (1.201 x 101)

6.9 ? 10-2 kg2
1.1 x 10-6
1.86 x 103
5.01 x 1022
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E. Temperature

• Temperature
• measure of the average KE of the particles in a
  sample of matter

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E. Temperature

• Convert these temperatures
• 25oC ______________K
• -15oF ______________ K
• 315K ______________ oC
• 288K ______________ oF

298.15
298
41.85
298
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F. Dimensional Analysis

• Dimensional Analysis is also called Unit Analysis
  and is a great way to solve problems in chemistry
  (or any time).

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F. Dimensional Analysis

• Dimensional Analysis
• A tool often used in science for converting units
  within a measurement system
• Conversion Factor
• A numerical factor by which a quantity expressed
  in one system of units may be converted to
  another system

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F. Dimensional Analysis Problem-Solving
Steps

• 1. Analyze
• 2. Plan
• 3. Compute
• 4. Evaluate

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F. Dimensional Analysis

• The Factor-Label Method
• Units, or labels are canceled, or factored out

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F. Dimensional Analysis

• Steps to solving problems
• 1. Identify starting ending units.
• 2. Line up conversion factors so units cancel.
• 3. Multiply all top numbers divide by each
  bottom number.
• 4. Check units answer.

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G. Conversion Factors

• Fractions in which the numerator and denominator
  are EQUAL quantities expressed in different units
• Example 1 in. 2.54 cm
• Factors 1 in. and 2.54 cm
• 2.54 cm 1 in.

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How many minutes are in 2.5 hours?

• Conversion factor
• cancel

60 min 1 hr
2.5 hr 1
150 min
x
By using dimensional analysis / factor-label
method, the UNITS ensure that you have the
conversion right side up, and the UNITS are
calculated as well as the numbers!
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G. Conversion Factors

• Write conversion factors that relate each of the
  following pairs of units
• 1. Liters and mL
• 2. Hours and minutes
• 3. Meters and kilometers

1000 mL 1 L
1 L 1000 mL

1 hr 60 min
1000 m 1 km
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H. SI Prefix Conversions

• 1. Memorize the following chart. (next slide)
• Find the conversion factor(s).
• Insert the conversion factor(s) to get to the
  correct units.
• When converting to or from a base unit, there
  will only be one step. To convert to or from any
  other units, there will be two steps.

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H. SI Prefix Conversions
Prefix
Symbol
Factor
move left
move right
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H. SI Prefix Conversions
0.532
532 m _______ km
NUMBER
UNIT
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H. SI Prefix Conversions
1 T(base) 1 000 000 000 000(base) 1012 (base)
1 G(base) 1 000 000 000 (base) 109 (base)
1 M(base) 1 000 000 (base) 106 (base)
1 k(base) 1 000 (base) 103 (base)
1 h(base) 100 (base) 102 (base)
1 da(base) 10 (base)
1 (base) 1 (base)
10 d(base) 1 (base)
100 c(base) 1 (base)
1000 m (base) 1 (base)
106 µ(base) 1 000 000 µ(base) 1(base)
109 n(base) 1 000 000 000 n(base) 1(base)
micro
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H. SI Prefix Conversions
1 m 100 cm

• a. cm to m
• b. m to µm
• c. ns to s
• d. kg to g

1 m 106 µm
1 s 109 ns
1 kg 1000 g
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H. SI Prefix Conversions

• 20 cm ______________ m
• 2) 0.032 L ______________ mL
• 3) 45 ?m ______________ m

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H. SI Prefix Conversions
8.05 x 1014

• 4) 805 Tb ______________ b

1012 b 1 Tb
805 Tb 1
805 x 1012 bytes
8.05 x 1014 bytes
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H. SI Prefix Conversions

• 5) 400. ?g ______________ kg
• 6) 57 Mm ______________ nm

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Dimensional Analysis Practice

• You have 7.25 in your pocket in quarters. How
  many quarters do you have?

38

• 2. How many seconds are in 1.4 days?
• Plan days hr min
  seconds

39

• 3. How many milliliters are in 1.00 quart of milk?

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1. You have 1.5 pounds of gold. Find its volume in
   cm3 if the density of gold is 19.3 g/cm3.

41

• 5. Your European hairdresser wants to cut your
  hair 8.0 cm shorter. How many inches will he be
  cutting off?

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• 6. Milton football needs 5.5 yards for a 1st
  down. How many cm is this?

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• 7. A piece of wire is 1.3 m long. How many
  1.5-cm pieces can be cut from this wire?

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• 8. How many liters of water would fill a
  container that measures 75.0 in3?