Convert 20 kilometers to METERS:

Convert 20 miles to METERS:

Convert 1.5 minutes to SECONDS:

s 90 s 605.1min 1

s 60min 1.5 min 1.5

Conversion of units: Section 1.5

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15cm cm

What is the length of the yellow bar?

Length = 9.7 cm

It makes NO sense to write Length = 9.73 cm, for example.

The significant digits of a measurement are all those digits that we know for sure, plus one more digit.

This last uncertain digit is the result of a careful estimate.

The significant digits of a measurement are all those digits that we know for sure, plus one more digit.

This last uncertain digit is the result of a careful estimate.

With respect to significant digits, remember:

1. Zeros to the left of the first number different than zero are NOT significant digits. Example: 0.0000071 has two significant digits (7 and 1).

2. Zeros to the right of a significant digit ARE significant. Examples: 230.0 has four significant digits; (0.05600 ± 0.00005) has four significant digits.

Sum and subtraction

We keep the number of decimals of the least precise quantity.

A+B+C = 140.261 140.3

A = 125.391 B = 12.7 C = 2.17B and C have 3 significant digits, but

C is more precise than B.

Product and division

We keep the number of significant digits of the least precise quantity.

A x B = 1592.4657 159 x 101

Number A has 6 significant digits, and is the most precise of the

numbers.

giga G 109 1 000 000 000 billion

mega M 106 1 000 000 million

kilo k 103 1 000 thousand

100 1 one

deci d 10-1 0.1 tenth

centi c 10-2 0.01 hundredth

milli m 10-3 0.001 thousandth

micro u 10-6 0.000 001 millionth

nano n 10-9 0.000 000 001 billionth

PREFIX SCIENTIFIC IN FIGURES IN WORDS NOTATION

We will adopt the international system of units which is the METRIC SYSTEM.

Instead of miles, feet, inches ---- meters

Instead of pounds, ounces ---- kilograms

This is in your

book: Table 1.4

It is to write numbers in terms of powers of 10

Examples:

number written in scientific notation how many significant digits?

234.37 2.3437 ×102 five significant digits

0.02 2 ×10-2 one significant digit

0.00430 4.30 ×10-3 three significant digits

Discussion about significant digits and scientific notation in your textbook: Section 1.4

Let’s CHANGE THE UNITS of these measurements:

L = 23 km L = _______ m

M = 10.3 kg M = _______ g

L = 224 m L = _______ km

M = 23 g M = _______ kg

L = 23 km L = _______ m

M = 10.3 kg M = _______ g

L = 224 m L = _______ km

M = 23 g M = _______ kg

L = 23 km L = 2.3 x 104 m

M = 10.3 kg M = 1.03 x 104 g

L = 224 m L = 0.224 km

M = 23 g M = 2.3 x 10-2 kg

L = 23 km L = 2.3 x 104 m

M = 10.3 kg M = 1.03 x 104 g

L = 224 m L = 0.224 km

M = 23 g M = 2.3 x 10-2 kg

Notice that we have to preserve the number of significant digits!!!Notice that we have to preserve the number of significant digits!!!

How to write RELATIVE ERRORS or UNCERTAINTIES:

error) (% t measuremen

error t measuremen

error) (% t measuremen

error t measuremen

You can express a measurement both ways:

Example:

(200 ± 5) cm

200 cm ± 2.5%

% 100tmeasuremen

erroryuncertaint %or error % % 100

tmeasuremen

erroryuncertaint %or error %

Error or uncertainty is

NOT A MISTAKE!

Every measurement

has an uncertainty, due

to the instrument used.

VERY useful relation in physics:

I call it “the rule of 3”: X1 Y1 X2 ?

X1· ? = X2·Y1

? = X2·Y1 ____X1

Mary eats 3 apples per day. How many apples will she have eaten in a week?

3 apples 1 day

? apples 7 days

3 · 7 = ? ·1

? = 21 apples

A year has 365 days.

How many years do I have

in 10 000 days?

1 year → 365 days

x years → 10 000 days

SAME UNITS!!! SAME UNITS!!!

Two important words in a lab:In the fields of science, engineering, industry and statistics, accuracy is the degree of closeness of a measured or calculated quantity to its actual (true) value.

Precision is also called reproducibility or repeatability, it is the degree to which further measurements or calculations show the same or similar results.

High accuracy, but low precision

High precision, but low accuracy

How do you check the accuracy of a measurement? By using different tools and methods of measurement.

How do you improve the precision of a measurement? By repeating the same measurement several times.

Experimental errors arise in two forms:

Random errors – Affect the PRECISION of the measurement.

Various sources: judgment in reading a measurement instrument, fluctuations in the conditions of the experiment; poorly defined quantity such as an uneven side of a block, etc.

How do we lessen the uncertainty from random errors? By repeating the measurements several times.

Systematic errors – Affect the ACCURACY of the measurement.

They are usually the same size of error in all measurements in a series: systematic error in the calibration of the measuring device, a flaw in the experiment such as the constant presence of friction, different temperature or pressure conditions, etc.

How do we estimate the systematic errors? By using a different experimental design and comparing the results.

For this course you are required to demonstrate adequate mathematical background.

For this course you are required to demonstrate adequate mathematical background.

Pre-requisite for PHY101:

Fundamentals of Pre-Calculus I (MAT124)

This is what you have learned in MA124 and will need again now:

• intermediate algebra (appendix A.3)

• trigonometry (appendix A.5)

• intermediate algebra appendix A.3 at the end of your book

• trigonometry appendix A.5 at the end of your book definitions of sin, cos, tan are in Chapter 1 (Section 1.8)

a) Some basic rules 8x = 32 x + 2 = 8 x / 5 = 9

b) Powers x2x4 = x6 x7 / x3 = x4

c) Factoring ax + ay + az = a(x + y + z)

d) Quadratic equations 3x2 + 8x – 10 = 0

e) Linear equations plot y = ax + b, where a is the slope of the line and b is the y-intercept.

f) Solving simultaneous linear equations 5x + y = –8 and 2x – 2y = 4 ; solve for y and x.

sin θ = sin2 θ + cos2 θ = 1

cos θ = sin 2θ = 2 sinθ cosθ

tan θ = cos 2θ = cos2θ – sin2θ

hypotenuse

θ opposite side

hypotenuse

θ toadjacent side

θ toadjacent side

θ opposite side

DO the Extra Credit assignment #1 !!!!!!!!!!!!

b

a

c

The following relationships apply to ANY triangle:

180

cos2222 bccba

cos2222 accab

cos2222 abbac sinsinsin

cba

Law of cosines:

Law of sines:

222 cba a

ONLY FOR THE RIGHT TRIANGLE:

b

cθ

θ is an angle in degrees

.

a

c

hypotenuse

side oppositeθsin

a

b

hypotenuse

adjacentθ cos

b

c

adjacent

opposite

cosθ

sinθθtan

Which one is a RIGHT TRIANGLE?