Transcript Unit Conversions

Base Units
• Metric System
•
-standard, used internationally(easy to
communicate through language barriers
•
-makes conversions simpler
•
-based on the number 10 & eliminates useless
memorization of numbers
• SI – System Internationale – revised metric
system, main difference is change to kg since
more common compared to grams
Common Base Units – units that can be measured
or altered using prefixes
MEASUREMENT
UNIT
SYMBOL
Length
meter
m
Mass
gram
g
Time
second
sec
Temperature
Kelvin
K
Volume of a Liquid
liter
L
Common Derived Units – units that must be
calculated using more than one measurement
MEASUREMENT
UNIT
SYMBOL
Volume of a solid
cubic centimeters
cm3
Density
grams per cm3 or mL
g/cm3 or g/mL
Unit 2
Common Prefixes – added to base units to change
their magnitude and make them more applicable.
PREFIX
SYMBOL
NUMERICAL
MEANING
Pico
p
1 × 10-12
Nano
n
1 × 10-9
Micro
µ
1 × 10-6
Milli
m
1 × 10-3
Centi
c
1 × 10-2
Deci
d
1 × 10-1
Deca
da
1 × 101
Hecto
H
1 × 102
Kilo
k
1 × 103
Mega
M
1 × 106
Unit
Conversions
Converting
Inches to centimeters
10.0 in
We start by writing down the
number and the unit
Converting
Inches to centimeters
10.0 in 2.54 cm
1 in
Our conversion factor for this is 1 in = 2.54 cm.
Since we want to convert to cm, it goes on the
top.
Converting
Inches to centimeters
10.0 in 2.54 cm
1 in
Now we cancel and collect units. The inches cancel
out, leaving us with cm –
the unit we are converting to.
Converting
Inches to centimeters
10.0 in 2.54 cm = 25.4 cm
1 in
Since the unit is correct,
all that is left to
do is the arithmetic...
The
Answer
Even though we have two different numbers
and two different units, they represent the
exact same length. You can check this by
looking at a ruler – find the 10 in mark and
directly across at the cm side. What number
do you find?
A more complex conversion
km to m
hr
s
In order to work a NSCI 110 homework
problem, we need to convert kilometers
per hour into meters per second. We
can do both conversions at once using
the same method as in the previous
conversion.
A more complex conversion
km to m
hr
s
80 km
hr
Step 1 –
Write down the
number and the
unit!
A more complex conversion
km to m
hr
s
80 km
1 hr
hr 3600 s
First we’ll convert time. Our conversion factor is
1 hour = 3600 sec. Since we want hours to cancel
out, we put it on the top.
A more complex conversion
km to m
hr
s
80 km
1 hr
1000 m
hr 3600 s 1 km
Next we convert our distance from kilometers to
meters. The conversion factor is 1 km = 1000 m.
Since we want to get rid of km, this time it goes
on the bottom.
A more complex conversion
km to m
hr
s
80 km
1 hr
1000 m
hr 3600 s 1 km
m
=
s
Now comes the important step – cancel and collect units.
If you have chosen the correct conversion factors, you
should only be left with the units you want to convert to.
A more complex conversion
km to m
hr
s
80 km
1 hr
1000 m
=
hr 3600 s 1 km
80,000 m
3600 s
Since the unit is correct, we
can now do the math – simply
multiply all the numbers on the
top and bottom, then divide the
two.
A more complex conversion
km to m
hr
s
80 km
1 hr
1000 m
=
hr 3600 s 1 km
80,000 m
m
= 22 s
3600 s
The
Answer!!
80 km/hr and 22 m/s are
both velocities. A car that is
moving at a velocity of
80 km/hr is traveling the
exact same velocity as a car
traveling at 22 m/s.
Unit 2
• Scientific Notation - a mathematical way to shorten
how we write very large or very small numbers. We
use exponents to show the power of 10 that we are
using.
• A positive exponent means a large number.
• A negative exponent means a small number.
• Rules: Move the decimal point until you have one
integer before the decimal. If you move it to the left
it is (+) to the right it is (-).
• Ex. 6023 - move decimal 3 places to left to make
6.023, now we have to add the power of 10 with the
exponent 103, so our final answer is 6.023 x 103.
Unit 2
• Ex. 2 .0000000345 , we move decimal to the right 8
spaces for 3.45 x 10-8.
• Calculations with Scientific Notation.
• Use your calculator! Learn how to punch numbers in.
You will have an EE or EXP key on your calculator,
you need to learn how to do this!
• Ex. 6.023 x 10 23 x 4.5 x 10 8 = ??
• Answer is 2.71 x 1032
• The sooner you learn how to do this, the better.
Precision vs. Accuracy
• Precision- getting the same results over and over
again
• Accuracy- getting the correct results over and over
again
• “you can have precision without accuracy but you
can’t have accuracy without precision”
• Percent error- tells you how close you are to the
true value
% error = │actual- theoretical│ x 100
actual
Significant Figures
Physical Science
What is a significant figure?
• There are 2 kinds of numbers:
– Exact: the amount of money in your
account. Known with certainty.
What is a significant figure?
- Approximate: weight, height—anything
MEASURED. No measurement is perfect.
– Always show every digit your are sure
of and one more that we consider
uncertain.
– Ex. 1.00 cm means we knew the 1 and
the .0, but after that we had to
estimate.
When to use Significant figures
• When a measurement is
recorded only those
digits that are
dependable are written
down.
When to use Significant figures
–If you measured the
width of a paper with
your ruler you might
record 21.7cm.
To a mathematician 21.70,
or 21.700 is the same.
But, to a scientist 21.7cm and
21.700 cm are NOT the same
• 21.700cm to a scientist
means the measurement
is accurate to within one
thousandth of a cm.
But, to a scientist 21.7cm and
21.70cm are NOT the same
• If you used an ordinary
ruler, the smallest
marking is the mm, so
your measurement has
to be recorded as
21.7cm.
How do I know how many Sig Figs?
• Rule: All digits are
significant starting with
the first non-zero digit
on the left.
How do I know how many Sig Figs?
• Exception to rule: In
whole numbers that end
in zero, the zeros at the
end are not significant.
How many sig figs?
•7
• 40
• 0.5
• 0.00003
• 7 x 105
• 7,000,000
•1
•1
•1
•1
•1
•1
How do I know how many Sig Figs?
nd
•2
Exception to rule: If
zeros are sandwiched
between non-zero digits,
the zeros become
significant.
How do I know how many Sig Figs?
• 3rd Exception to rule: If
zeros are at the end of a
number that has a
decimal, the zeros are
significant.
How do I know how many Sig Figs?
• 3rd Exception to rule:
These zeros are showing
how accurate the
measurement or
calculation are.
How many sig figs here?
•
•
•
•
•
•
1.2
2100
56.76
4.00
0.0792
7,083,000,000
•
•
•
•
•
•
2
2
4
3
3
4
How many sig figs here?
•
•
•
•
•
•
3401
2100
2100.0
5.00
0.00412
8,000,050,000
•
•
•
•
•
•
4
2
5
3
3
6
What about calculations with
sig figs?
• Rule: When adding or
subtracting measured
numbers, the answer can have
no more places after the
decimal than the LEAST of
the measured numbers.
Add/Subtract examples
• 2.45cm + 1.2cm = 3.65cm,
• Round off to
= 3.7cm
• 7.432cm + 2cm = 9.432
round to
 9cm
Multiplication and Division
• Rule: When multiplying
or dividing, the result
can have no more
significant figures than
the least reliable
measurement.
A couple of examples
• 56.78 cm x 2.45cm = 139.111
• Round to
 139cm2
• 75.8cm x 9.6cm = ?
2
cm
Oreo Lab
• Your group will be given a sample of
regular and double stuff Oreos.
• Do not Eat them! (yet)
• Scientifically prove, both by mass and by
volume whether or not the double stuff is
actually a double stuff. V= ∏r2 x h
• Must have data and proof.
• You will use a scale and a small protractor
ruler as your measuring devices.
• Record everything in a chart and write your
conclusion. Good luck!
The End
Have Fun Measuring and
Happy Calculating!
Dimensional Analysis Quiz
1.
2.
3.
4.
5.
6.
75 mL =____dm3
10 miles = ____ km
500 mm =_____ cm
500 mL =_____ L
24 km/hr = _____ mi/hr
.45 kg/L = _____ g/mL