1. Chapter 1
Measurement
F. Morales

2. CHAPTER OUTLINE Scientific Method Measurements/SI Units
Volume & Density
Conversion of Units
Scientific Notation
Significant Figures

3. The Nature of Science —Scientific Method
Science is NOT a body of knowledge, but a method to understand nature & how it works
Science accepts nothing on faith
The ultimate judge is always the experiment
Many observations over time
From trends, we come up w/Models or HYPOTHESIS
Require further testing, EXPERIMENT
Results CONTRADICT: descard Hypothesis
Results AGREE w/prediction: Hypothesis needs to survive more experiments to be accepted as a good description of nature

4. SCIENTIFIC METHOD
The scientific method is a process of creative thinking and testing aimed at objective and verifiable discoveries.
Knowledge gained through the scientific method is self-correcting and improves over time.

5. MEASUREMENTS SI UNITS
Measurements are made by scientists to determine size, length and other properties of matter.
For measurements to be useful, a measurement standard must be used.
A standard is an exact quantity that people agree to use for comparison.
SI is the standard system of measurement used worldwide by scientists.

6. SI BASE UNITS Quantity Measured Units Symbol Length Meter m Mass
Kilogram kg
Time
Seconds s
Temperature
Kelvin K
Electric current
Ampere A
Amount of substance
Mole
mol
Intensity of light
Candela cd

7. DERIVED UNITS
In addition to the base units, several derived units are commonly used in SI system.
Quantity Measured
Units
Symbol
Volume
Liter L
Density
grams/cc
g/cm3

8. VOLUME
Volume is the amount of space an object occupies.
Common units are cm3 or liter (L) and milliliter (mL).
1 mL = 1 cm3
1 L = 1000 mL

9. Which has greatest density?
Density is mass per unit volume of a material.
Common units are g/cm3 (solids) or g/mL (liquids).
Density is indirectly related to the volume of an object.
Density is directly related to the mass of an object.
Which has greatest density?

10. CONVERSION OF UNITS
The SI system of units is easy to use because it is based on multiples of ten.
Common prefixes are used with the base units to indicate the multiple of ten that the unit represents.
Prefixes
Symbol
Multiplying factor
mega- M
1,000,000
kilo- k
1000
centi- c
0.01
milli- m
0.001
micro- 
0.000,001

11. CONVERSION OF UNITS 100000 or 105 How many mm are in a cm?
How many cm are in a km?
10x10x10x10x10 10

12. CONVERSION OF UNITS final unit beginning unit Conversion factor
Any unit can be converted into another by use of the appropriate conversion factor.
final unit
beginning unit
Conversion factor

13. Example 1:
The length of a football field is 100 yards. What is the length of the field in meters? (1m = yd) 1
100 yd
91.4 m
1.094

14. Example 2:
The thickness of a book is 2.5 cm. What is this measurement in mm? 10
2.5 cm
25 mm 1

15. Example 3: How many centimeters are in 2.0 ft? (1 in = 2.54 cm) 12

16. Example 4: How many seconds are there in 1 day? 24 60 60 1 day 1 1 1

17. Example 5:
If the density of gold is 19.3 g/cm3, how many grams does a 5.00 cm3 nugget weigh?
19.3
96.5 g
5.00 cm3 1

18. Example 6:
What volume of mercury has a mass of 60.0 g if its density is 13.6 g/mL? 1
60.0 g
4.41 mL
13.6

19. IS UNIT CONVERSION IMPORTANT?
In 1999 Mars Climate orbiter was lost in space because engineers failed to make a simple conversion from English units to metric, an embarrassing lapse that sent the $125 million craft fatally close to the Martian surface.
Further investigation showed that engineers at Lockheed Martin, which built the aircraft, calculated navigational measurements in English units. When NASA’s JPL engineers received the data, they assumed the information was in metric units, causing the confusion.

20. A x 10n SCIENCTIFIC NOTATION
Scientific Notation is a convenient way to express very large or very small quantities.
Its general form is
A x 10n
n = integer
coefficient
1 < A < 10

21. SCIENTIFIC NOTATION
To convert from decimal to scientific notation:
Move the decimal point so that it’s located after the first nonzero digit.
Follow the new number by a multiplication sign and 10 with an exponent (power).
The exponent is equal to the number of places that the decimal point was shifted.
7.5 x 10 7

22. SCIENTIFIC NOTATION
For numbers smaller than 1, the decimal moves to the left and the power becomes negative. 3
6.42 x 10

23. Write 6419 in scientific notation.
Example 1:
Write 6419 in scientific notation.
decimal after first nonzero digit
power of 10
6.419 x 103
6419.

24. Write 0.000654 in scientific notation.
Example 2:
Write in scientific notation.
power of 10
decimal after first nonzero digit
6.54 x 10-4

25. CALCULATIONS WITH SCIENTIFIC NOTATION
To perform multiplication or division with scientific notation:
Change numbers to exponential form.
Multiply or divide coefficients.
Add exponents if multiplying, or subtract exponents if dividing.
If needed, reconstruct answer in standard exponential form.

26. Multiply coefficients Convert to exponential form
Example 1:
Multiply 30,000 by 600,000
Add exponents
Reconstruct answer
Multiply coefficients
Convert to exponential form 9
(3 x 104)
(6 x 105) =
18 x 10
1.8 x 1010

27. Convert to exponential form
Example 2:
Divide 30,000 by 0.006
Reconstruct answer
Subtract exponents
Divide coefficients
Convert to exponential form
(3 x 104) 3
(3 x 104) /
(6 x 10-3) =
= x 104-(-3)
(6 x 10-3) 6 7
= 0.5 x 10
5 x 106

28. SIGNIFICANT FIGURES Two kinds of numbers are used in science:
Counted or defined:
exact numbers; have no uncertainty
Measured:
are subject to error; have uncertainty
Every measurement has uncertainty because of instrument limitations and human error.

29. UNCERTAINTY IN MEASUREMENTS
8.65
8.6
uncertain
certain
What is this measurement?
What is this measurement?
The last digit in any measurement is the estimated one.

30. SIGNIFICANT FIGURES RULES
Significant figures are the certain and uncertain digits in a measurement.
All non-zero digits are significant.
All sandwiched zeros are significant.
Leading zeros (before or after a decimal) are NOT significant.
Trailing zeros (after a decimal) are significant.

31. Examples:
Determine the number of significant figures in each of the following measurements: g
461 cm
3 sig figs
5 sig figs
0.006 m
1025 g
1 sig fig
4 sig figs
0.705 mL
5500 km
2 sig figs
3 sig figs

32. ROUNDING OFF NUMBERS
If rounded digit is less than 5, the digit is dropped.
51.234
Round to 3 sig figs
Round to 4 sig figs
Less than 5
Less than 5

33. ROUNDING OFF NUMBERS
If rounded digit is equal to or more than 5, the digit is increased by 1.
51.369
51.369
Round to 3 sig figs 4
5.4505
5.4505 1
Round to 4 sig figs
More than 5
Equal to 5

34. SIGNIFICANT FIGURES & CALCULATIONS
The results of a calculation cannot be more precise than the least precise measurement.
In multiplication or division, the answer must contain the same number of significant figures as in the measurement that has the least number of significant figures.

35. MULTIPLICATION & DIVISION
Calculator answer
4 sig figs
3 sig figs
(9.2)(6.80)(0.3744) =
2 sig figs
The answer should have two significant figures because 9.2 is the number with the fewest significant figures.
The correct answer is 23

36. SIGNIFICANT FIGURES & CALCULATIONS
The results of an addition or a subtraction must be expressed to the same precision as the least precise measurement.
The result must be rounded to the same number of decimal places as the value with the fewest decimal places.

37. ADDITION & SUBTRACTION
Add 83.5 and 23.28
83.5
23.28
Least precise number
Calculator answer
106.78
106.8
Correct answer

38. Example 1: 5.008 + 16.2 + 13.48 = 34.688 7 Least precise number
Round to

39. Example 2:
3 sig figs
6.1788 2
Round to
2 sig figs

40. THE END