Convert 20 kilometers to METERS:

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Convert 20 kilometers to METERS
Conversion of units Section 1.5
Convert 20 miles to METERS
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Significant digits
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.
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• With respect to significant digits, remember
• 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).
• 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.

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How to / - x with significant digits?
A 125.391 B 12.7 C 2.17
B and C have 3 significant digits, but C is more
precise than B.
Number A has 6 significant digits, and is the
most precise of the numbers.
Sum and subtraction We keep the number of
decimals of the least precise quantity. ABC
140.261 140.3
Product and division We keep the number of
significant digits of the least precise
quantity. A x B 1592.4657 159 x 101
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We will adopt the international system of units
which is the METRIC SYSTEM. Instead of miles,
feet, inches ---- meters Instead of pounds,
ounces ---- kilograms
PREFIX SCIENTIFIC IN
FIGURES IN WORDS
NOTATION
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
This is in your book Table 1.4
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Scientific notation
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
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Lets 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 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!!!
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How to write RELATIVE ERRORS or UNCERTAINTIES
You can express a measurement both ways
Example (200 5) cm 200 cm 2.5
Error or uncertainty is NOT A MISTAKE! Every
measurement has an uncertainty, due to the
instrument used.
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VERY useful relation in physics
I call it the rule of 3
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A year has 365 days. How many years do I have
in 10 000 days?
1 year ? 365 days x years ? 10 000 days
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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.
accuracy
How do you check the accuracy of a measurement?
By using different tools and methods of
measurement.
precision
Precision is also called reproducibility or
repeatability, it is the degree to which further
measurements or calculations show the same or
similar results.
How do you improve the precision of a
measurement? By repeating the same measurement
several times.
High accuracy, but low precision
High precision, but low accuracy
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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.
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• 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)

For this course you are required to demonstrate
adequate mathematical background.
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This is a PHYSICS course NOT a mathematics
course Math will be used as a tool that you
already know We sympathize that math can be
hard, therefore sometimes we will show problems
in slow steps. But do not expect that always. You
must then catch up at home, tutoring or office
hours.
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• 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)

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

1. Some basic rules 8x 32 x 2 8 x / 5 9
2. Powers x2x4 x6 x7 / x3 x4
3. Factoring ax ay az a(x y z)
4. Quadratic equations 3x2 8x 10 0
5. Linear equations plot y ax b, where a is the
   slope of the line and b is the y-intercept.
6. Solving simultaneous linear equations 5x y 8
   and 2x 2y 4 solve for y and x.

sin ? sin2 ? cos2 ? 1 cos ? sin
2? 2 sin? cos? tan ? cos 2? cos2?
sin2?
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The following relationships apply to ANY
triangle
Law of cosines
Law of sines
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Which one is a RIGHT TRIANGLE?
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