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CHAPTER 3: SCIENTIFIC
MEASUREMENT Mrs. Brayfield
MEASUREMENTS
What are examples of different measurements that
you take?
How easy is it to express those numbers?
How about expressing a number like:
1,000,000,000,000
0.0000000000036
Not so easy…
SCIENTIFIC NOTATION
Scientific notation is an easy way to express very
large or very small numbers
To write scientific notation you write the given
number as the multiplication of a coefficient and 10
raised to a power
So from the previous slide:
1,000,000,000,000 1.0 X 1012
0.0000000000036 3.6 X 10-12
ACCURACY AND PRECISION
Accuracy is a measure of how close the
measurement comes to the actual (or true) value of
whatever is measured
Precision is a measure of how close a series of
measurements are to each other
ACCURACY AND PRECISION
ERROR
When making measurements, there is a difference
between the “true” value and the measured value
This is what error is
the difference between the two values
Another name for the “true” value is the accepted
value and another name for the measured value is
the experimental value
ERROR
We measured the temperature of a pot of boiling water
to be 99.1°C, but the actual value should be 100°C
What is the actual value?
100°C
What is the experimental value?
99.1°C
What is the error for our measurement?
Error = Experimental Value – Actual Value = 99.1°C – 100°C
Error = -0.9°C
PERCENT ERROR
In chemistry, we typically like to know our percent
error of a calculation or experiment
The percent error formula is:
Remember that |error| means that you take the
absolute value of the error
SIGNIFICANT FIGURES
Significant figures is where scientists report all
useful information
Measurements must be reported to the right
number of significant figures so that proper
calculations can be made with them
Significant figures helps us determine the error in our
measurement
SIGNIFICANT FIGURES
When taking a measurement, how many decimal
places do we need to go for…
A thermometer with increments of 1°C?
A thermometer with increments of 0.5°C?
A balance with increments of 0.01 g?
A graduated cylinder with increments of 10 mL?
SIGNIFICANT FIGURES
Instead of taking a measurement, sometimes you
will be given a math problem where you must report
your number with the correct significant figures
There are 5 rules to follow when finding the number
of significant figures
SIGNIFICANT FIGURES RULES
1. Every nonzero digit is significant
2. Zeros between nonzero digits are significant
3. Leftmost zeros in front of nonzero digits are not
significant
4. Zeros to the right of nonzero digits are significant
5. If a number is counted or if a quantity is exactly
defined, then all digits are significant
SIGNIFICANT FIGURES RULES
1. Every nonzero digit is significant
For example the following all have three significant
figures: 24.7 meters, 0.743 meters, 714 meters
2. Zeros between nonzero digits are significant
For example the following all have four significant
figures: 7003 meters, 40.79 meters, 1.503 meters
SIGNIFICANT FIGURES RULES
3. Leftmost zeros in front of nonzero digits are not
significant
For example the following all have two significant
figures:
0.0071 meter = 7.1x10-3 meter
0.42 meter = 4.2x10-1 meter
0.000099 meter = 9.9x10-5 meter
4. Zeros to the right of nonzero digits are significant
For example the following all have four significant
figures: 43.00 meters, 1.010 meters, 9.000 meters
SIGNIFICANT FIGURES RULES
5. If a number is counted or if a quantity is exactly
defined, then all digits are significant
For example, you could count 23 people in a
classroom. Since this is a counted value it has an
unlimited number of significant figures. The same goes
for say 60 min = 1 hr (each number has an unlimited
number of significant figures).
* When making calculations, just ignore the number
of significant figures from those values.
SIGNIFICANT FIGURES RULES
1. Every nonzero digit is significant
2. Zeros between nonzero digits are significant
3. Leftmost zeros in front of nonzero digits are not
significant
4. Zeros to the right of nonzero digits are significant
5. If a number is counted or if a quantity is exactly
defined, then all digits are significant
CALCULATIONS USING SIGNIFICANT FIGURES
In calculations the answer cannot be more precise than
the least precise measurement
Addition and Subtraction:
The answer should be rounded to the same number of
decimal places as the measurement with the least number of
decimal places
Multiplication and Division:
The answer should be rounded to the same number of
significant figures as the measurement with the least
significant figures
UNITS
What units do we measure everyday things with?
Why are units important?
The International System of Units (SI) tells us the
internationally accepted units of different
measurement
This is the metric system
The metric system is based on multiples of 10
THE METRIC SYSTEM
LENGTH
Length is measured in meters (m)
VOLUME
Volume is measured in liters (L)
MASS
Mass is measured in kilograms (kg)
TEMPERATURE
What is temperature?
It tells us how hot or cold something is
There are three temperature scales:
Fahrenheit
Celsius
Kelvin
CELSIUS AND KELVIN SCALES
The Celsius scale sets the freezing temperature of
water at 0°C and the boiling point of water at 100°C
The Kelvin scale sets the freezing temperature of
water at 273 K and the boiling point at 373 K
Notice that the degree sign is not used in Kelvin (K)
CELSIUS AND KELVIN SCALES
Notice that a change in one degree Celsius is equal
to a change in one degree Kelvin
CELSIUS AND KELVIN SCALES
To convert between the scales, use the following
formula:
Remember that to convert from Fahrenheit to
Celsius the formula is:
DENSITY
http://phet.colorado.edu/sims/density-and-
buoyancy/density_en.html
DENSITY
Density is the ratio of mass of an object to its
volume
Density is an intensive property that depends only
on the composition of a substance, not on the size
of the sample
CONVERSIONS
If I told you that the conversion rate from dollars to
Euros was 1 Euro for every 1.5 dollars and you
were going on a trip that cost $4500 dollars, how
many Euros would you need?
CONVERSIONS
A conversion factor is a ratio of equivalent
measurements
This means that the top number in the ratio is equal to
the bottom number
We can use this method for converting between
different units
DIMENSIONAL ANALYSIS
Dimensional analysis is a way to analyze and solve
problems using the units (or dimensions) of the
measurements.
