Transcript Math Skills for the Science Lab notes

Math Skills for the Laboratory
“SI“
The InternationalSystem
Unit
Unit
Unit
Unit
Unit
of length...Meter
of
mass...Gram
of
volume...Liter
of
t e m p . . . 00 C e l s i u s
of
time...Second
The order of prefixes
in the metric system,
for every power of ten
from 3 to -3, is
Kilometer,
Hectometer,
Decameter,
Meter,
Decimeter,
Centimeter,
Millimeter
You can remember it
by thinking of…
King
Hector
Distributed
Money…
Dollars &
Cents to
Millie
1000 or 103
Changing
the Size
of Units
100 or 102
10 or 101
1 or 100
0.1 or 10-1
0.01 or
10-2
0.001 or 10-3
Length, Width, and Height
• Length is the (longest) distance from side to side
between an object’s ends.
• Width is the distance from side to side, across the
object from side to side at right angles to the length.
• Height is the vertical (top to bottom) distance
between an object’s ends.
Mass
• The amount of matter or stuff in something
• Not to be confused with weight!
– Which is the pull of the earth’s gravity on an
object.
• Weight can change but the amount of
matter in an object stays the same.
Mass
•A triple-beam (pan) balance or an electronic balance
is used to measure mass.
•The unit we use is grams (g.).
Volume
• The amount of space an object occupies.
Volume of a cube or rectangular prism.
• Measure the length,
width, and height of
the object.
• Then, multiply the
three measurements.
• V= l x w x h
• The units are cm3.
height
Volume of an Irregularly
Shaped Object
•A graduated
cylinder is used to
find the volume of
an irregularly
shaped object.
•The unit we use is
milliliters (mL).
How do I find the volume of an
irregularly shaped object?
Use the water displacement method.
1. Fill a graduated cylinder with
water & record the amount.
2. Put the object in the water
& record the new amount.
3. Find the difference.
volume of water & object
– volume of water
----------------------------------volume of object
Temperature
• Temperature is a measure of how
fast the atoms and molecules of a
substance are moving.
– The faster the movement, the hotter
the object’s temperature.
– The slower the movement, the cooler
the object’s temperature.
• Temperature is measured, using a
thermometer, in degrees on the
Fahrenheit, Celsius, and Kelvin
scales.
– In science we use Celsius (°C).
(Fahrenheit is sometimes used in
meteorology…the study of weather.)
Time
• Seconds (s) are used to
measure the duration of
an event (how long it
took).
• We use a stopwatch to
measure time.
Derived measurements are made
up of more than one measurement
• Ex.
Change in field value ft
– Gradient =
Distance
m
– Density = Mass
volume
g
mL
Derived measurements have “compound” units…more than one type of unit.
Density
• The relationship between the mass and
volume of an object. In other words, how
tightly packed the matter is inside the object.
– Example - a classroom with 35 students has a
higher density than one with 5 students….
• Changing the size (volume) of an object
does not change its density!!!!!!!!!!!!!!!!!!!!
– It is still made up of the same type of matter!
Density and Water
An object with a density less than
1.0 g/mL will float in water.
The density of water is 1.0 g/mL.
An object with a density greater
than 1.0 g/mL will sink in water.
How do I find the density of an object?
use these units
• Density = mass
grams
--------------------------------------------------
volume
mL or cm3
DON’T FORGET: Round to the nearest tenth.
Density Problems
Find the density of an object whose mass is
50.0 g and volume is 25.0 mL.
D = 50.0 g
25.0 mL
D = 2.0 g/mL
The density triangle
You can use the density triangle to figure out
any of the variables if you already know
two of them.
M
÷
D
X
V
Use the density triangle
• Mass = 20.0 g
• Density = 0.5 g/mL
• Volume = ?
40.0 mL
• Volume = 10.0 cm3
• Density = 0.7 g/cm3
• Mass = ?
7.0 g
Percent Deviation (Error)
• A way of comparing a measurement with the
most commonly accepted value for that
measurement. (How far off your answer is
from the “correct” answer.” or “How accurate
you answer is.”)
% error = your result - accepted value x 100 %
accepted value
Accuracy vs. Precision
Precise =
repeated
measurements
are close to
each other
Accurate =
close to the
accepted value
(“bulls-eye”)
Your goal is to
be both
accurate and
precise.
How many cm is this pencil?
With a more precise scale, how many?
Scientific Notation
A short-hand way of writing very large
or very small numbers without writing
all of the zeros.
Coefficient – any number from greater than zero and
less than ten
Exponent – shows the number of times we move the
decimal point (represents the # of times 10’s are
multiplied together. Ex. 10210
=  10 = 100
)
The Distance From the Sun to
the Earth
93,000,000 miles
Changing from Standard Notation
to Scientific Notation
Step 1: for a number = to or
greater than 1
• Move decimal left
• Leave only one number in front of decimal
Step 2
• Write number without zeros
Step 3
• Count how many places you moved decimal
• Make that your power of ten
– Since you moved the decimal point to the left, your
exponent will be positive.
The power of
ten is positive 7
because
the decimal
moved 7 places to
the left.
93,000,000 --Standard Form
9.3 x 107 --Scientific Notation
Example
• Given: 289,800,000
• Use: 2.898 (moved 8 places to the left)
• Answer: 2.898 x 108
Practice Problems
Write in scientific notation.
Decide the power of ten.
1)
2)
3)
4)
98,500,000 = 9.85 x 10?
64,100,000,000 = 6.41 x 10?
279,000,000 = 2.79 x 10?
4,200,000 = 4.2 x 10?
9.85 x 107
6.41 x 1010
2.79 x 108
4.2 x 106
More Practice Problems
For these, decide where the decimal will be moved.
1) 734,000,000 = ______ x 108
2) 870,000,000,000 = ______x 1011
3) 90,000,000,000 = _____ x 1010
1) 7.34 x
108
2) 8.7 x
1011
3) 9 x 1010
Complete Practice Problems
Write in scientific notation.
1) 50,000
2) 7,200,000
3) 802,000,000,000
1) 5 x 104
2) 7.2 x 106
3) 8.02 x 1011
The length of an E. coli bacterium
0.0000021 m
Changing from Standard Notation
to Scientific Notation
Step 1: for a number less than 1
but greater than zero
*Move decimal to the right
*Leave only one number in front of decimal
0.0000021 = 0000002.1
Step 2
• Write number without zeros
0000002.1 = 2.1
Step 3
• Count how many places you moved decimal
• Make that your power of ten
– Since you moved the decimal point to the right, your
exponent will be negative.
The power of ten is negative 6
because the decimal moved
6 places to the right.
Example
• Given: 0.000567
• Use: 5.67 (moved 4 places)
• Answer: 5.67 x 10-4
Since the original number was less than 1,
the exponent is negative.
Changing Numbers in Scientific
Notation to Standard Notation
1. If the exponent is (+) move the decimal to the
right the same number of places as the exponent.
a. 1.65  101 = 16.5
b. 1.65  103 = 1650
2. If the exponent is (-) move the decimal to the left
the same number of places as the exponent.
a. 4.6  10-2 = 0.046
b. 1.23  10-3 = 0.00123
Scientific Notation to Standard Form
Move the decimal to the right
3.4 x 105 in scientific notation
3.40000 --- move the decimal
right 5 places
340,000 in standard form
Move the decimal to the left
3.4 x 10-5 in scientific notation
00003.4 --- move the decimal
left 5 places
0.00003.4 in standard form
Write in Standard Form
•
•
•
•
6.27 x 106
9.01 x 104
6.27 x 10-6
9.01 x 10-4
•
•
•
•
6,270,000
90,100
0.0000067
0.000901