WHAT IS MEASUREMENT?
• Comparing one object to a standard
• In science, we use SI Units
• meters, oC, grams NOT oF, pounds, ounces etc.
TWO TYPES OF MEASUREMENTS
1. Qualitative = descriptive and non-numerical
• EX: color, odor, texture, etc
2. Quantitative = definite form, numbers and units
• EX: temperature, mass, length, volume, density
SCIENTIFIC NOTATION
• Used to write very big and very small numbers
• 6.02 X 1023 instead of 602000000000000000000000
• Number is written as the product of 2 numbers: a
coefficient and 10 raised to a power
• N X 10x
• N is a coefficient; a number that is between 1 and ten
• X is an integer
SCIENTIFIC NOTATION RULES
• Only one digit to the left of the decimal
• Exponents
• if the # is greater than one, the exponent is positive
• if the # is less than one, the exponent is negative
• In your calculator, use “EE” or “EXP” for the “x 10 ^”
• EX: 6.02 x 1023 in calculator = 6.02 EE 23
2 500 000 000
Step #1: Insert an understood decimal point
.
Step #2: Decide where the decimal must end
up so that one number is to its left
Step #3: Count how many places you bounce
the decimal point
1 2 3 4 5 6 7 8 9
Step #4: Re-write in the form M x 10n
2.5 X 109
CONVERTING A NUMBER INTO SCIENTIFIC NOTATION
The exponent is
the number of
places we
moved the
decimal.
CONVERTING A NUMBER INTO SCIENTIFIC NOTATION
The exponent is positive because the
number we started with was greater
than 1.
2 500 000 000
2.5 X 109
CONVERTING A NUMBER INTO SCIENTIFIC NOTATION
Step #1 Locate the decimal
Step #2 Decide where the decimal must end up so that
one number is to its left
Step #3 count how many places you bounce the
decimal point
Step #4 Re-write in the form N x 10x
1 2 3 4 5
CONVERTING A NUMBER INTO SCIENTIFIC NOTATION
The exponent is negative because the
number we started with was less than 1.
CHEM-LOG…CONVERT THE FOLLOWING
• 45000 written as
• 510 written as
• 602000 written as
• 4.5 x 10 -4 written as
• 3.2 x 10 -2 written as
• 2.89 x 10 -3 written as
4.5 x 10 4
5.3 x 10 2
6.02 x 10 5
0.00045
0.032
0.00289
If you moved the decimal point to the left, your exponent is positive
If you moved to the right, your exponent is negative
PERFORMING CALCULATIONS WITH SCIENTIFIC NOTATION
• Addition and Subtraction
• If the exponents are the same, add the coefficients
• Keep the exponent the same in the answer
PERFORMING CALCULATIONS WITH SCIENTIFIC NOTATION
• Addition and Subtraction
• If the exponents are NOT the same, we must first move
a decimal to make them the same
• Keep the exponent the same in the answer
PERFORMING CALCULATIONS WITH SCIENTIFIC NOTATION
• GET USED TO USING YOUR CALCULATOR…
2.5 x 104 x 3.2 x 108
5.7 x 104 ÷ 8.9 x 108
PERFORMING CALCULATIONS WITH SCIENTIFIC NOTATION
• GET USED TO USING YOUR CALCULATOR…
2.5 x 10-7 x 3.2 x 10-2
5.7 x 10-3 ÷ 8.9 x 10-1
UNCERTAINTY IN MEASUREMENT
• Accuracy = a measure of how close a
measurement comes to the actual or true value of
whatever is measured
• Precision = a measure of how close a series of
measurements are to one another
Precise, not
accurate
UNCERTAINTY IN MEASUREMENT
Accurate, not
precise
UNCERTAINTY IN MEASUREMENT
Not precise,
not accurate
UNCERTAINTY IN MEASUREMENT
Precise AND
accurate
ERROR IN MEASUREMENT
• Accepted/actual value = the correct value based
on reliable references
• Experimental value = the value measure in the lab
• Error = accepted – experimental
• % error = I accepted – experimental I x 100
accepted
CALCULATING ERROR
• If you only make 33 cookies and the recipe says you
should make 36, what is your percent error?
Percent Error = I accepted – experimental I x 100
accepted
accepted = 36
experimental = 33
Percent Error = I 36-33 I x 100
36
= 8.3 % error
SIGNIFICANT FIGURES
• Numbers that include ALL digits that can be known
plus a last digit that is estimated
• Digits that have meaning
SIGNIFICANT FIGURES
•Rules regarding zeros • Every non-zero digit is significant (567)
• Zeros between non-zeros are sig (305)
• Zeros in front of nonzeros are
placeholders…NOT SIG (0.00035)
• Zeros following a nonzero only sig if • The come after a decimal point (3.4210)
• Or a decimal follows (3420.)
• 3420
SIGNIFICANT FIGURES
• HOW MANY SIG FIGS??????
4.21
4.210
0.0421
42.10
4210
42010
42010.0
(3)
(4)
(4)
(3)
(3)
(4)
(6)
SIGNIFICANT FIGURES IN CALCULATIONS
• How many significant figures do you need to give in
your answer?
• Answers cannot be more precise than the least
precise measurement
• FOR EXAMPLE, divide 21.4 by 9.8…what’s your answer?
• Answer in calculator says 2.183673469
SIGNIFICANT FIGURES IN CALCULATIONS
• Adding and subtracting • The last digit in your answer is set by the first doubtful digit
• For Example:
0.200
1.2
+ 3.400
4.800
Answer should
only have one
significant digit
to the right of the decimal
point
Therefore, the
answer should
be
4.8
SIGNIFICANT FIGURES IN CALCULATIONS
• Multiplying and dividing
• Answer contains no more sig figs that the least accurate
measurement
• For example:
3.2 x 7.81542 = 25.009344
Answer should
only have two
sig figs
Therefore, the
answer should
be
25
SIGNIFICANT FIGURES IN CALCULATIONS
Rounding
• If the digit immediately following the last sig fig is less
than 5, drop all digits after the last sig fig
• If the digit is 5 or greater, the value of the digit in the
last sig place is increased (rounded) by 1
0.1710
1.2
+ 3.490
4.8610
Answer should
only have one
significant digit
to the left of the decimal point
The number that
follows the 8 is
greater than 5 so
drop it…answer is 4.9
INTERNATIONAL SYSTEM OF UNITS (SI)
• Revised version of the metric system
• Seven base units
• length, mass, temp, time, amount, light intensity, electric current
• Derived units can be calculated using base units
• density, volume, pressure
SI UNITS
• Length: meter (m)
• Mass: kilogram (kg)
• Temperature: kelvin (K)
• Time: second (s)
• Quantity: mole (mol)
• Luminosity: candela (cd)
• Current: ampere (A)
DERIVED UNITS - VOLUME
• Volume = the space occupied by any sample of
matter
• Derived from length measurements
• V = l x w x h
• Can also be measured by volume displacement
• Units
• cubic meter (m3) or cubic cm (cm3)
• 1cm3 = 1ml
DERIVED UNITS - DENSITY
• Defined: ratio of an object’s mass to its volume
• Equation: D = m/V
• Units: g/cm3
DENSITY PROBLEM #1
• A copper penny has a mass of 3.1 g and a volume
of 0.35 cm3. What is the density of copper?
Equation: D = m/V
Units: g/cm3
DENSITY PROBLEM #2
• A student finds a shiny piece of metal that she thinks is
aluminum. In the lab, she determines that the metal has
a volume of 245 cm3 and a mass of 612 g. Calculate the
density. Is it aluminum? Density Al= 2.70 g/cm3
Equation: D = m/V
Units: g/cm3
TEMPERATURE
• Defined: direction of heat transfer
• When two objects are in contact, heat moves from the object
at the higher temperature to the object at the lower
temperature
TEMPERATURE SCALES
• Celsius
• Uses two determined temperatures as reference temp
• Boiling point of water = 100oC
• Freezing point of water = 0 oC
• Kelvin scale
• Boiling point of water = 373 K
• Freezing point of water = 273 K
• Notice no degree sign
• 0 K = absolute zero or the point at which all motion stops
CONVERTING BETWEEN CELSIUS AND KELVIN
K = oC + 273
Ex: convert 25 oC to K
K = 25 oC + 273
K = 298K
oC = K - 273
Ex: convert 0K to oC
oC = 0K - 273
oC = -273 oC
METRIC SYSTEM
• Americans measure in feet, inches, yards, etc.
• Based on the king
• Yard = length of the king’s arm
• Foot = length of the king’s foot
• Pound = amount of marble the king could pick up with one hand
• New king = new standards
• The rest of the world measure using the metric system
• Based on powers of 10
METRIC PREFIXES
Prefix Symbol Scientific
Notation
Meaning
Mega- M 106 Million times
kilo- k 103 thousand times
hecto- h 102 Hundred times
deca- da 101 Ten times
BASE ~ ~ Base Unit
deci- d 10-1 1 / tenth
centi- c 10-2 1 / hundredth
milli- m 10-3 1 / thousandth
METRIC PREFIXES
Prefix Symbol Scientific
Notation
Pnemonic Device
Mega- M 106 Most
kilo- k 103 Kittens
hecto- h 102 Hate
deca- da 101 Dogs
BASE ~ ~ Because
deci- d 10-1 Dogs
centi- c 10-2 Can’t
milli- m 10-3 Meow !
DIMENSIONAL ANALYSIS
• a way to analyze and solve problems using the units
or dimensions of the measurements
CONVERSION FACTOR
• Relationships between two measurements that
allow you to convert from one unit to another
• Ex: 1 yr = 365 days, 1 day = 24 hours
3 STEPS TO SOLVING PROBLEMS
ACE Method
1. Analyze
• Identify what is given, unknown, make a plan
2. Calculate
• Substitute values and use algebra to solve
3. Evaluate
• Does the answer make sense?
SAMPLE PROBLEM #1
How many days are there in 6 weeks?
You are looking
for this!
This is your “given”.
ANALYZE
Figure out what relationships you
will have to know in order to
convert from 1 unit to another.
1 week = 7 days
CONVERSION FACTOR
Conversion Factor : top and bottom must be
equal in value
days week 1
days 7x weeks 6
CANCELING UNITS
6 weeks x = 42 days 1 week
7 days
Cancel units : cancel
units to leave correct
units for the answer
Calculate : multiply
across top and bottom
and divide to get final
answer
SET UP THE PROBLEM
• Given: 4 hours, 65 miles = 1 hour
• Unknown: how many miles?
• ANALYZE the DIMENSIONS
If you have hours and want miles, your conversion
factor should be arranged to CANCEL hours and
LEAVE miles
SAMPLE PROBLEM #2
1. Write your Given “over one” 4 hours
1
2. “times a line” 4 hours x _______
1
3. To cancel hours, the conversion factor must have hours on the BOTTOM
4 hours x _______
1 1 hour
4. Conversion factor must have desired unit on TOP
4 hours x 65 miles 1 1 hour
= 260 miles
SAMPLE PROBLEM #3
• If you just turned 17 years old, how many seconds
old are you?
Given: 17 years old
Unknown: seconds old
Conversion factors: 1 yr = 365.25 days 1 day = 24 hrs 1 hr = 60 min 1 min = 60 s
SAMPLE PROBLEM #3
• Solve:
17 yr x 365.25 day x 24 hr x 60 min x 60 s =
1 yr 1 day 1 hr 1 min
When solving dimensional analysis problems, multiply by everything in the numerator and then divide by everything in the denominator and hit enter only ONCE!!
In calculator:
17 x 365.25 x 24 x 60 x 60 ÷ 1 ÷ 1 ÷ 1 ÷ 1 =
SAMPLE PROBLEM #3
•Answer: 17 yrs = 536,479,200 s
•Check: Does this answer make
sense?
• Yes! 17 years should be a lot of
seconds!
SAMPLE PROBLEM #4
• If you are traveling 50 miles per hour, how many
feet per second are you going?
Given: 50 miles per hour
Unknown: feet per second
Conversion factors: 1 mile = 5280 ft 1 hr = 60 min 1 min = 60 s
SAMPLE PROBLEM #4
• Solve:
50 miles x 5280 feet x 1 hrx x 1 min=
1 hour 1 mile 60 min 60 sec
In calculator:
50 x 5280 x 1 x 1 ÷ 1 ÷ 1 ÷ 60 ÷ 60 = 73 feet/sec