Contributed by:

The highlights are:

1. Math and units

2. Scientific notation

3. Unit conversion

4. Accuracy

5. Precision

6. Significant figures

1. Math and units

2. Scientific notation

3. Unit conversion

4. Accuracy

5. Precision

6. Significant figures

1.
Units

and

Measurement

Physics

Mr. Berman

International Space Station

and

Measurement

Physics

Mr. Berman

International Space Station

2.
It All Starts with a Ruler!!!

3.
Math and Units

• Math- the language of Physics

• SI Units – International System

– MKS

• Meter m

• Mass kg

• Time s

• National Bureau of Standards

• Prefixes

• Math- the language of Physics

• SI Units – International System

– MKS

• Meter m

• Mass kg

• Time s

• National Bureau of Standards

• Prefixes

4.
SI Unit Prefixes - Part I

Name Symbol Factor

tera- T 1012

giga- G 109

mega- M 106

kilo- k 103

hecto- h 102

deka- da 101

Name Symbol Factor

tera- T 1012

giga- G 109

mega- M 106

kilo- k 103

hecto- h 102

deka- da 101

5.
SI Unit Prefixes- Part II

Name Symbol Factor

deci- d 10-1

centi- c 10-2

milli- m 10-3

micro- μ 10-6

nano- n 10-9

pico- p 10-12

femto- f 10-15

Name Symbol Factor

deci- d 10-1

centi- c 10-2

milli- m 10-3

micro- μ 10-6

nano- n 10-9

pico- p 10-12

femto- f 10-15

6.
The Seven Base SI Units

Quantity Unit Symbol

Length meter m

Mass kilogram kg

Temperature kelvin K

Time second s

Amount of mole mol

Luminous Intensity candela cd

Electric Current ampere a

Quantity Unit Symbol

Length meter m

Mass kilogram kg

Temperature kelvin K

Time second s

Amount of mole mol

Luminous Intensity candela cd

Electric Current ampere a

7.
Derived SI Units (examples)

Quantity unit Symbol

Volume cubic meter m3

Density kilograms per kg/m3

cubic meter

Speed meter per second m/s

Newton kg m/ s2 N

Energy Joule (kg m2/s2) J

Pressure Pascal (kg/(ms2) Pa

Quantity unit Symbol

Volume cubic meter m3

Density kilograms per kg/m3

cubic meter

Speed meter per second m/s

Newton kg m/ s2 N

Energy Joule (kg m2/s2) J

Pressure Pascal (kg/(ms2) Pa

8.
SI Unit Prefixes for Length

Name Symbol Analogy

gigameter Gm 109

megameter Mm 106

kilometer km 103

decimeter dm 10-1

centimeter cm 10-2

millimeter mm 10-3

micrometer μm 10-6

nanometer nm 10-9

picometer pm 10-12

Name Symbol Analogy

gigameter Gm 109

megameter Mm 106

kilometer km 103

decimeter dm 10-1

centimeter cm 10-2

millimeter mm 10-3

micrometer μm 10-6

nanometer nm 10-9

picometer pm 10-12

9.
• 9 min video about powers of 10 in length.

• http://powersof10.com/film

• http://powersof10.com/film

10.
Scientific Notation

M x 10n

• M is the coefficient 1• 10 is the base

• n is the exponent or power of 10

M x 10n

• M is the coefficient 1

• n is the exponent or power of 10

11.
Other Examples:

• 5.45E+6 or

• 5.45 x 10^6

• 5.45E+6 or

• 5.45 x 10^6

12.
Numbers less than 1 will have a

negative exponent.

A millionth of a second is:

0.000001 sec 1x10-6

1.0E-6 1.0^-6

negative exponent.

A millionth of a second is:

0.000001 sec 1x10-6

1.0E-6 1.0^-6

13.
Factor-Label Method of Unit

Conversion

• Example: Convert 5km to m:

• Multiply the original measurement by a

conversion factor.

NEW UNIT

85km x 1,000m = 85,000m

1km

OLD UNIT

Conversion

• Example: Convert 5km to m:

• Multiply the original measurement by a

conversion factor.

NEW UNIT

85km x 1,000m = 85,000m

1km

OLD UNIT

14.
Factor-Label Method of Unit

Conversion: Example

• Example: Convert 789m to km:

789m x 1km =0.789km= 7.89x10-1km

1000m

Conversion: Example

• Example: Convert 789m to km:

789m x 1km =0.789km= 7.89x10-1km

1000m

15.
Convert 75.00 km/h to m/s

75.00 km x 1000 m x 1 h___ = 20.83m/s

h 1 km 3600 s

75.00 km x 1000 m x 1 h___ = 20.83m/s

h 1 km 3600 s

16.
Limits of Measurement

• Accuracy and Precision

• Accuracy and Precision

17.
• Accuracy - a measure of how

close a measurement is to the

true value of the quantity being

measured.

close a measurement is to the

true value of the quantity being

measured.

18.
Example: Accuracy

• Who is more accurate when

measuring a book that has a true

length of 17.0cm?

17.0cm, 16.0cm, 18.0cm, 15.0cm

15.5cm, 15.0cm, 15.2cm, 15.3cm

• Who is more accurate when

measuring a book that has a true

length of 17.0cm?

17.0cm, 16.0cm, 18.0cm, 15.0cm

15.5cm, 15.0cm, 15.2cm, 15.3cm

19.
• Precision – a measure of how

close a series of measurements

are to one another. A measure of

how exact a measurement is.

close a series of measurements

are to one another. A measure of

how exact a measurement is.

20.
Example: Precision

Who is more precise when measuring

the same 17.0cm book?

17.0cm, 16.0cm, 18.0cm, 15.0cm

15.5cm, 15.0cm, 15.2cm, 15.3cm

Who is more precise when measuring

the same 17.0cm book?

17.0cm, 16.0cm, 18.0cm, 15.0cm

15.5cm, 15.0cm, 15.2cm, 15.3cm

21.

22.
Example: Evaluate whether the

following are precise, accurate or

both.

Accurate Not Accurate Accurate

Not Precise Precise Precise

following are precise, accurate or

both.

Accurate Not Accurate Accurate

Not Precise Precise Precise

23.
Significant Figures

• The significant figures in a

measurement include all of the

digits that are known, plus one

last digit that is estimated.

• The significant figures in a

measurement include all of the

digits that are known, plus one

last digit that is estimated.

24.
Centimeters and Millimeters

25.
Finding the Number of Sig Figs:

• When the decimal is present, start counting

from the left.

• When the decimal is absent, start counting

from the right.

• Zeroes encountered before a non zero digit

do not count.

• When the decimal is present, start counting

from the left.

• When the decimal is absent, start counting

from the right.

• Zeroes encountered before a non zero digit

do not count.

26.
How many sig figs?

100 10302.00

10302 1.0302x104

100 10302.00

10302 1.0302x104

27.
Sig Figs in Addition/Subtraction

Express the result with the same

number of decimal places as the

number in the operation with the least

decimal places.

Ex: 2.33 cm

+ 3.0 cm

5.3 cm

(Result is rounded to one decimal place)

Express the result with the same

number of decimal places as the

number in the operation with the least

decimal places.

Ex: 2.33 cm

+ 3.0 cm

5.3 cm

(Result is rounded to one decimal place)

28.
Sig Figs in Multiplication/Division

• Express the answer with the same sig

figs as the factor with the least sig

figs.

• Ex: 3.22 cm

x 2.0 cm

6.4 cm2

(Result is rounded to two sig figs)

• Express the answer with the same sig

figs as the factor with the least sig

figs.

• Ex: 3.22 cm

x 2.0 cm

6.4 cm2

(Result is rounded to two sig figs)

29.
Counting Numbers

• Counting numbers have infinite sig

figs.

• Ex: 3 apples

• Counting numbers have infinite sig

figs.

• Ex: 3 apples

30.
Solving Word Problems

• Analyze

– List knowns and unknowns.

– Draw a diagram.

– Devise a plan.

– Write the math equation to be used.

• Calculate

– If needed, rearrange the equation to solve for the

unknown.

– Substitute the knowns with units in the equation and

express the answer with units.

• Evaluate

– Is the answer reasonable?

• Analyze

– List knowns and unknowns.

– Draw a diagram.

– Devise a plan.

– Write the math equation to be used.

• Calculate

– If needed, rearrange the equation to solve for the

unknown.

– Substitute the knowns with units in the equation and

express the answer with units.

• Evaluate

– Is the answer reasonable?