1. Chapter 3 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

4. A. Accuracy vs. Precision

5. B. Percent Error your value given value
Indicates accuracy of a measurement
your value
given value

6. B. Percent Error % error = 2.94 %
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.
% error = 2.94 %

7. 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

8. C. Significant Figures 739 5085 2.60 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
Trailing zeros without a decimal point -- 2,500
739
5085
2.60

9. Counting Sig Fig Examples
C. Significant Figures
Counting Sig Fig Examples
4 sig figs
3 sig figs
3. 5,280
3. 5,280
3 sig figs
2 sig figs

10. C. Significant Figures (13.91g/cm3)(23.3cm3) = 324.103g 324 g
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) = g
4 SF
3 SF
3 SF
324 g

11. C. Significant Figures 3.75 mL + 4.1 mL 7.85 mL 3.75 mL + 4.1 mL
Calculating with Sig Figs (con’t)
Add/Subtract - The # with the lowest decimal value determines the place of the last sig fig in the answer
3.75 mL mL
7.85 mL
3.75 mL mL
7.85 mL
 7.9 mL

12. C. Significant Figures Calculating with Sig Figs (con’t)
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

13. C. Significant Figures Practice Problems 5. (15.30 g) ÷ (6.4 mL)
4 SF
2 SF
= g/mL
 2.4 g/mL
2 SF g g
 18.1 g
18.06 g

14. 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 atoms
coefficient
exponent

15. D. Scientific Notation 65,000 kg  6.5 × 104 kg
Converting into Sci. Notation:
Move decimal until there’s 1 digit to its left. Places moved = exponent
Large # (>1)  positive exponent Small # (<1)  negative exponent
Only include sig figs – all of them!

16. D. Scientific Notation Practice Problems
7. 2,400,000 g kg  10-5 km  104 mm
2.4  106 g
2.56  10-3 kg km
62,000 mm

17. D. Scientific Notation (5.44 × 107 g) ÷ (8.1 × 104 mol) =
Calculating with Sci. Notation
(5.44 × 107 g) ÷ (8.1 × 104 mol) =
Type on your calculator:
EXP EE
EXP EE
ENTER
EXE
5.44 7
8.1 ÷ 4 =
= 670 g/mol
= 6.7 × 102 g/mol

18. D. Scientific Notation Practice Problems 4  1010 cm2 6.9  10-2 kg2
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

19. Temperature Conversions
CH. 3 - MEASUREMENT
Temperature Conversions

20. A. Temperature Temperature
measure of the average KE of the particles in a sample of matter

21. Temperature 298.15 298 41.85 298 Convert these temperatures:
25oC = ______________K
-15oF = ______________ K
315K = ______________ oC
288K = ______________ oF
298.15
298
41.85
298

22. Measurement
Dimensional Analysis

23. A. Problem-Solving Steps
1. Analyze 2. Plan 3. Compute 4. Evaluate

24. B. 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

25. B. Dimensional Analysis
The “Factor-Label” Method
Units, or “labels” are canceled, or “factored” out

26. B. 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.

27. C. Conversion Factors Example: 1 in. = 2.54 cm
Fractions in which the numerator and denominator are EQUAL quantities expressed in different units
Example: in. = 2.54 cm
Factors: 1 in and cm
2.54 cm in.

28. How many minutes are in 2.5 hours?
Conversion factor cancel
2.5 hr 1 x
60 min
1 hr
= 150 min
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!

29. C. Conversion Factors 1. Liters and mL 2. Hours and minutes
Write conversion factors that relate each of the following pairs of units:
1. Liters and mL
2. Hours and minutes
3. Meters and kilometers
1 L
1000 mL
1000 mL
1 L =
1 hr
60 min
1000 m
1 km

30. D. 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.

31. A. SI Prefix Conversions
Symbol
Factor
tera- T
1012
giga- G
109
mega- M
106
kilo- k
103
hecto- h
102
deka- da
101
move left
move right
BASE UNIT
---
100
deci- d
10-1
centi- c
10-2
milli- m
10-3
micro- 
10-6
nano- n
10-9

32. A. SI Prefix Conversions=
532 m = _______ km
0.532
NUMBER
UNIT
NUMBER
UNIT

33. D. SI Prefix Conversions
1 T(base) = (base) = 1012 (base)
1 G(base) = (base) = 109 (base)
1 M(base) = (base) = 106 (base)
1 k(base) = (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) = µ(base) = 1(base)
109 n(base) = n(base) = 1(base)
micro

34. D. 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

35. D. SI Prefix Conversions
20 cm = ______________ m
2) L = ______________ mL
3) 45 m = ______________ m

36. D. SI Prefix Conversions
4) 805 Tb = ______________ b
Terabytes
bytes
805 Tb 1
1012 b
1 Tb
= 805 x 1012 bytes 
= 8.05 x 1014 bytes

37. D. SI Prefix Conversions
5) 400. g = ______________ kg 6) 57 Mm = ______________ nm

38. E. Dimensional Analysis Practice
You have $7.25 in your pocket in quarters. How many quarters do you have?

39. E. Dimensional Analysis Practice
2. How many seconds are in 1.4 days?
Plan: days hr min seconds

40. E. Dimensional Analysis Practice
3. How many milliliters are in 1.00 quart of milk?

41. E. Dimensional Analysis Practice
You have 1.5 pounds of gold. Find its volume in
cm3 if the density of gold is 19.3 g/cm3.

42. E. Dimensional Analysis Practice
5. Your European hairdresser wants to cut your hair 8.0 cm shorter. How many inches will he be cutting off?

43. E. Dimensional Analysis Practice
6. Milton football needs 550 cm for a 1st down. How many yards is this?

44. E. Dimensional Analysis Practice
7. A piece of wire is 1.3 m long. How many 1.5-cm pieces can be cut from this wire?

45. E. Dimensional Analysis Practice
8. How many liters of water would fill a container that measures 75.0 in3?