1. Unit 1- Introduction to Physics

2. Learning Objectives Know the SI system base units
Convert within the metric system & to English system & vice versa
Convert using dimensional (unit) analysis
Know what significant figures are and how to determine s.f. for multiplication/division and addition/subtraction
Read a graph to find slope
From graph shapes determine relationships
From math equations, determine relationships
Solve problems using order of magnitude and percent error
Basic statistics

3. The Metric System
The metric system is an internationally standardized system of units of measurement.
The metric system is based on a base unit and prefixes.

4. International System (SI)
A. Quantities and base units of measure
length – meter, m
temperature – Kelvin
mass – gram
time – second
B. Derived quantities and units
electric current – ampere
Force- Newton (kg.m/s2)
Amount of substance – mole
Luminous intensity – candela

5. Prefixes Kilo - 1000 k Hecto - 100 h Deca - 10 da 1 Deci - 0.1 d
Centi c
Milli m
Micro µ

6. Length The basic unit of length in the metric system is the meter (m)
Metric Units of Length
Kilometer (km) = 1000 m
Hectometer (hm) = 100 m
Decameter (dam) = 10 m
Meter (m) = 1 m
Decimeter (dm) = 0.1 m
Centimeter (cm) = 0.01 m
Millimeter (mm) = m

7. Mass
Weight is a measure of how strongly gravity is pulling on an object (decreases as elevation increases)
Mass is the amount of material in an object (doesn’t change)
Note: on Earth, weight and mass are used interchangeably

8. Mass The basic unit of mass in the metric system is a gram (g)
1 g = mass of water in a cube that measures 1 cm x 1 cm x 1cm
Metric Units of Mass
Kilogram (kg) = 1000 g
Hectogram (hg) = 100 g
Decagram (dag) = 10 g
Gram (g) = 1 g
Decigram (dg) = 0.1 g
Centigram (cg) = 0.01 g
Milligram (mg) = g

9. Capacity/Volume
Liquid substances are measured in units of capacity/volume
The basic unit of mass in the metric system is a liter (L)
1 L = capacity of a cube that measures 10 cm x 10 cm x 10 cm
Metric Units of Capacity
Kiloliter (kL) = 1000 L
Hectoliter (hL) = 100 L
Decaliter (daL) = 10 L
Liter (L) = 1 L
Deciliter (dL) = 0.1 L
Centiliter (cL) = 0.01 L
Milliliter (mL) = L

10. Equivalences Units of Weight Units of Capacity Units of Length
1 oz g
1 lb g
2.2 lb kg
Units of Capacity
1.06 qt L
1 gal L
Units of Length
1 in = 2.54 cm
3.28 ft m
1.09 yd m
1 mi km

11. Dimensional Analysis
Dimensional Analysis (also called Factor-Label Method or the Unit Factor Method) is a problem-solving method that uses the fact that any number or expression can be multiplied by one without changing its value (Multiplication Property of 1 – the Magic One)
Use the units to dictate the form of the Magic One

12. Rules for Making T charts
1. Decide whether you are converting using the metric system (prefixes) or American system. Go to step 2 if you are using the metric system.
2. Convert to base units( i.e. g,

13. Metric Conversion 1 Ex. Convert 20 kg to g
1 x 10^3g
20 x 10 ^3 g
1 kg

14. Metric Conversion 2 Ex. Convert 20kg to mg

15. Ex: Convert 130 lbs to kg (round to the nearest whole number)
Write the original measurement as a unit fraction
Multiply the unit fraction by a magic one – the form of which is dictated by the units
the numerator unit is the unit you want
the denominator unit is the unit you want to eliminate
Write your answer in the specified form (decimal number)

16. Ex: Convert 130 lbs to kg (round to the nearest whole number)

17. Ex: Convert 60 km to mi (round to the nearest whole number)
Write the original measurement as a unit fraction
Multiply the unit fraction by a magic one – the form of which is dictated by the units
the numerator unit is the unit you want
the denominator unit is the unit you want to eliminate
Write your answer in the specified form (decimal number)

18. Ex: Convert 60 km to mi (round to the nearest whole number)

19. Ex: Convert 5.4 kg to lb (round to the nearest tenth place)
Write the original measurement as a unit fraction
Multiply the unit fraction by a magic one – the form of which is dictated by the units
the numerator unit is the unit you want
the denominator unit is the unit you want to eliminate
Write your answer in the specified form (decimal number)

20. Ex: Convert 5.4 kg to lb (round to the nearest tenth place)

21. Ex: Convert 45 cm to in (round to the nearest tenth place)
Write the original measurement as a unit fraction
Multiply the unit fraction by a magic one – the form of which is dictated by the units
the numerator unit is the unit you want
the denominator unit is the unit you want to eliminate
Write your answer in the specified form (decimal number)

22. Ex: Convert 45 cm to in (round to the nearest tenth place)

23. Significant Figures
When using our calculators we must determine the correct answer; our calculators are mindless drones and don’t know the correct answer.
There are 2 different types of numbers
Exact
Measured
Exact numbers are infinitely important
Measured number = they are measured with a measuring device (name all 4) so these numbers have ERROR.
When you use your calculator your answer can only be as accurate as your worst measurement…Doohoo 
Chapter Two

24. Exact Numbers
An exact number is obtained when you count objects or use a defined relationship.
Counting objects are always exact 2 soccer balls 4 pizzas
Exact relationships, predefined values, not measured 1 foot = 12 inches 1 meter = 100 cm
For instance is 1 foot = inches? No
1 ft is EXACTLY 12 inches.

25. Definitions 1. counting 2. definition
A. Exact numbers are obtained by
1. counting
2. definition
B. Measured numbers are obtained by
1. using a measuring tool

26. Solution A. Exact numbers are obtained by 2. counting 3. definition
B. Measured numbers are obtained by
1. using a measuring tool

27. Learning Check Classify each of the following as an exact or a
measured number.
1 yard = 3 feet
The diameter of a red blood cell is 6 x 10-4 cm.
There are 6 hats on the shelf.
Gold melts at 1064°C.

28. 2.4 Measurement and Significant Figures
Every experimental measurement has a degree of uncertainty.
The volume, V, at right is certain in the 10’s place, 10mL<V<20mL
The 1’s digit is also certain, 17mL<V<18mL
A best guess is needed for the tenths place.
Chapter Two

29. What is the Length? We can see the markings between 1.6-1.7cm
It is over 1.65, but less then 1.68, therefore it is between.
We can’t see the markings between the .6-.8
We must guess between .6 & .8
We record 1.67 cm as our measurement
The last digit an 7 was our guess...stop there

30. Learning Check What is the length of the wooden stick? 1) 4.5 cm

31. ?
8.00 cm or 3 (2.2/8)

32. Measured Numbers
Do you see why Measured Numbers have error…you have to make that Guess!
All but one of the significant figures are known with certainty. The last significant figure is only the best possible estimate.
To indicate the precision of a measurement, the value recorded should use all the digits known with certainty.

33. Below are two measurements of the mass of the same object
Below are two measurements of the mass of the same object. The same quantity is being described at two different levels of precision or certainty.
Chapter Two

34. Note the 4 rules
When reading a measured value, all nonzero digits should be counted as significant. There is a set of rules for determining if a zero in a measurement is significant or not.
RULE 1. Zeros in the middle of a number are like any other digit; they are always significant. Thus, g has five significant figures.
RULE 2. Zeros at the beginning of a number are not significant; they act only to locate the decimal point. Thus, cm has three significant figures, and mL has four.
Chapter Two

35. RULE 3. Zeros at the end of a number and after the decimal point are significant. It is assumed that these zeros would not be shown unless they were significant m has six significant figures. If the value were known to only four significant figures, we would write m.
RULE 4. Zeros at the end of a number and before an implied decimal point may or may not be significant. We cannot tell whether they are part of the measurement or whether they act only to locate the unwritten but implied decimal point.
Chapter Two

36. Practice Rule #1 Zeros 6 3 5 2 4
All digits count
Leading 0’s don’t
Trailing 0’s do
0’s count in decimal form
0’s don’t count w/o decimal
0’s between digits count as well as trailing in decimal form
48000.
48000
3.982106

37. 2.5 Scientific Notation
Scientific notation is a convenient way to write a very small or a very large number.
Numbers are written as a product of a number between 1 and 10, times the number 10 raised to power.
215 is written in scientific notation as:
215 = 2.15 x 100 = 2.15 x (10 x 10) = 2.15 x 102
Chapter Two

38. Two examples of converting standard notation to scientific notation are shown below.
Chapter Two

39. Two examples of converting scientific notation back to standard notation are shown below.
Chapter Two

40. Scientific notation is helpful for indicating how many significant figures are present in a number that has zeros at the end but to the left of a decimal point.
The distance from the Earth to the Sun is 150,000,000 km. Written in standard notation this number could have anywhere from 2 to 9 significant figures.
Scientific notation can indicate how many digits are significant. Writing 150,000,000 as 1.5 x 108 indicates 2 and writing it as x 108 indicates 4.
Scientific notation can make doing arithmetic easier. Rules for doing arithmetic with numbers written in scientific notation are reviewed in Appendix A.
Chapter Two

41. 2.6 Rounding Off Numbers
Often when doing arithmetic on a pocket calculator, the answer is displayed with more significant figures than are really justified.
How do you decide how many digits to keep?
Simple rules exist to tell you how.
Chapter Two

42. Once you decide how many digits to retain, the rules for rounding off numbers are straightforward:
RULE 1. If the first digit you remove is 4 or less, drop it and all following digits becomes 2.4 when rounded off to two significant figures because the first dropped digit (a 2) is 4 or less.
RULE 2. If the first digit removed is 5 or greater, round up by adding 1 to the last digit kept is 4.6 when rounded off to 2 significant figures since the first dropped digit (an 8) is 5 or greater.
If a calculation has several steps, it is best to round off at the end.
Chapter Two

43. Practice Rule #2 Rounding
Make the following into a 3 Sig Fig number
Your Final number must be of the same value as the number you started with,
129,000 and not 129
1.5587
1367
128,522
106
1.56
.00374
1370
129,000
1.67 106

44. Examples of Rounding 0 is dropped, it is <5
For example you want a 4 Sig Fig number
0 is dropped, it is <5
8 is dropped, it is >5; Note you must include the 0’s
5 is dropped it is = 5; note you need a 4 Sig Fig
780,582
1999.5
4965
780,600
2000.