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Scientific Measurement
A measurement is a quantity that has both
a number and a unit
Some numbers encountered in science can
be either very large or very small
We use scientific notation to make those
numbers easier to work with.
Scientific Measurement
In scientific notation, a given number is written as a coefficient and an exponent
The coefficient is a number more than 1, but less than 10
6 300 000.
94 700.
0.000 008
0.00 736
Scientific Measurement
In chemistry, the meanings of accuracy and
precision are quite different.
Accuracy is a measure of how close a
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 one another, irrespective of
the actual value.
Scientific Measurement
To evaluate the accuracy of a
measurement, the measured value must be
compared to the correct value.
To evaluate the precision of a
measurement, you must compare the
values of two or more repeated
measurements.
Scientific Measurement
Good Accuracy,
Good Precision
Poor Accuracy,
Good Precision
Poor Accuracy,
Poor Precision
The closeness of a dart to the bull’s-eye corresponds to the degree of accuracy. The closeness of several darts to one another corresponds to the degree of precision.
Scientific Measurement
There is a difference between the accepted
value, which is the correct value for the
measurement based on reliable references, and
the experimental value, the value measured in
the lab.
Percent error indicates the difference between
the accepted and experimental values
Percent Error = |Accepted-Experimental|
Accepted Value X 100
Scientific Measurement
This estimated number, 22.9°C, has
three digits. The first two digits (2 and 2) are
known with certainty, while the
rightmost digit (9) has been estimated
and involves some uncertainty.
These reported digits all convey useful
information, however, and are called
significant figures.
Scientific Measurement
The significant figures in a
measurement include all of the digits
that are known, plus a last digit that
is estimated.
There are six rules to determine if a
number is significant.
Scientific Measurement
1. Every nonzero digit in a reported measurement is assumed to be significant.
24.7 meters
2. Zeros appearing between nonzero digits are significant.
7003 meters
Scientific Measurement
3. Leftmost zeros appearing in front of nonzero digits
are not significant.
0.0071 meters
0.0901 meters
4. Zeros at the end of a number and to the right of a
decimal point are always significant.
43.00 meters
0.010 meters
Scientific Measurement
5. Zeros at the rightmost end of a measurement without a decimal point are not significant.
7000 meters
27,210 meters
To make 7000 meters have four significant figures we must add a decimal point - 7000. meters
6. There are two situations in which numbers have an unlimited number of significant figures.
A number that is counted is exact: 21 students in class Exactly defined quantities: 60 min = 1 hr
Scientific Measurement
How many significant figures are in each measurement?
a. 123 m
b. 40506 mm
c. 9.8000 x 104 m
d. 22 metersticks
e. 0.070 80 m
f. 98000 m
Scientific Measurement
In general, a calculated answer cannot be
more precise than the least precise
measurement from which it was
calculated. It must be rounded to make it consistent with
the measurements from which it was
calculated.
Scientific Measurement
For an addition or subtraction calculation The answer should be rounded to the same number of
decimal places (not digits) as the measurement with
the least number of decimal places.
a. 12.52 meters + 349.0 meters + 8.24 meters
b. 74.626 meters – 28.34 meters
Scientific Measurement
For a multiplication and division
calculation The answer should be rounded to the same
number of significant figures as the
measurement with the least number of
significant figures.
a. 7.55 meters x 0.34 meter
b. 0.365 meter2 ÷ 0.0200 meter
Scientific Measurement
The International System of Units
(abbreviated SI) is a revised version of
the metric system. The SI units were adopted by international
agreement in 1960.
SI units are used for consistency among the
scientific community
Scientific Measurement There are seven SI base
units.
From these base units,
all other SI units of
measurement can be
derived. Derived units are used for
measurements such as
volume, density, and
pressure.
SI Base Units
Quantity SI base
unit
Symbol
Length meter m
Mass kilogram kg
Temperature kelvin K
Time second s
Amount of
substance mole mol
Luminous
intensity candela cd
Electric
current ampere A
Scientific Measurement
Each SI unit is based on a measurable
standard They are not arbitrary units
Sometimes it is necessary to modify the
base unit using a prefix. Some prefixes make units larger and others make
units smaller
Scientific Measurement
Small Metric Prefixes
Prefix Symbol Factor
deci d 0.1
centi c 0.01
milli m 0.001
micro μ 0.000 001
nano n 0.000 000 001
Large Metric Prefixes
Prefix Symbol Factor
giga G 1 000 000 000
mega M 1 000 000
kilo k 1000
•Although, the derived SI unit for volume is m3, we
commonly use the liter (L)
1 cm3 = 1 mL
Scientific Measurement
A conversion factor is a ratio of
equivalent measurements. The measurement in the numerator is
equivalent to the measurement in the
denominator. Therefore you actually multiplying by 1
Conversion factors are useful in solving
problems in which a given measurement must
be expressed in some other unit of measure.
Scientific Measurement
Conversion factors within a system of
measurement are defined quantities or exact
quantities. Therefore, they have an unlimited number of significant
figures and do not affect the rounding of a calculated
answer.
Scientific Measurement
Weight and mass are two different measurements
Weight is a force that measures the pull on a given mass by gravity.
Mass is the measure of the amount of matter.
Scientific Measurement
Scientists commonly use two equivalent units of temperature, the degree Celsius (˚C) and the kelvin (K).
The Celsius scale sets the freezing point of water
at 0°C and the boiling point of water at 100°C. On the Kelvin scale, the freezing point of water is
273.15 kelvins (K), and the boiling point is 373.15 K.
Scientific Measurement
The Kelvin scale is based on absolute
zero
Absolute zero is the point where particle
motion seizes
Absolute zero is 0 Kelvin
Scientific Measurement
Because one degree on the Celsius scale is equivalent to one kelvin on the Kelvin scale, converting from one temperature to another is easy.
You simply add or subtract 273, as shown in the following equations.
K = °C + 273
°C = K – 273
Scientific Measurement
Density is the ratio of the mass of an object to its volume.
Density is an intensive property
The volume of most substances increases as the temperature increases, while the mass remains the same.
Since density is the ratio of an object’s mass to its volume, the density of a substance generally decreases as its temperature increases.
Water is an important exception.
mass
volume
Density =
Scientific Measurement
Calculating Density
A copper penny has a mass of 3.10 g and a
volume of 0.35 cm3. What is the density of
copper?
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