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2 Measurements and Calculations, 2.1 Scientific Notation, 2.2 Units, 2.3…
2 Measurements and Calculations
Scientific Notation is a method of making very large or very small numbers more compact and easier to write
numbers are either very large or very small
125=1.25x100
this is because 100=10x10= 10 prime we can say 125=1.25x100= 1.25x10 prime
scientific notation
is simply expresses a number as a product of a number between 1 and 10 and the appropriate power of 10
the best way to determine the appropriate power of 10 is to count the number of decimal places.
whenever the decimal is moved to the left the exponent is positive
whenever the decimal is moved to the left the exponent is negative
Units
are the part of a measurement that tells us what scale or standard is being used to represent the results of the measurement.
trade requires units
units measure quantities like
mass
length,
Temperature
time
there are three separate unit systems used in the world
the
English system
that is used by the United States
The
Metric System
used by most of the industrialized world
the
International system (SI)
used by scientists
the units are based on the metric system and they derive from there
these measurements consist of a unit and a number and both are equally important
the SI system uses prefixes to change the size of the units
Measurements
a
meter
is a little longer than a yard
meters are the fundamental unit of IS
Fractions of a meter or multiplies of a meter can be expressed in powers of 10
Volume
is the amount of three-dimensional space occupied by a substance
the fundamental unit of volume in the SI system is based on the volume of a cube that measures 1 meter in each of the three directions
this measurement is one cubic meter
a
liter
is slightly larger than a quart
it represents one square in a cubic meter
one cubic centimeter is called a
millimeter
mass
can be described as the quantity of matter present in an object.
the fundamental SI mass unit is the
kilogram
the prefixes for various mass units are based on the
gram
measurements are not always exact
we must sometimes compensate for the lack of clarity with our measuring devices with estimations
sometimes we must imagine where a measurement is due to a lack of tic marks on our unit of measurement.
certain numbers are numbers that are the same regardless of human error
measurements always have some degree of uncertainty
this uncertainty depends on the measuring device
numbers recorded in a measurement are called
significant
figures
significant figures include all the certain numbers plus the first uncertain number.
the number of sig figs is determined by the uncertainty of the measuring device.
Significant Figures rules
nonzero integers. nonzero integers always count as significant figures.
zeros. there are three classes of zeros
a.leading zeroes are zeroes that precede all of the nonzero digits. they never count as sig figs
b. captive zeroes are zeroes that fall between nonzero digits. they always count as sig figs.
c.trailing zeros are zeros at the right end of the number, they are only significant if the number is written with a decimal point.
3.Exact numbers. often calculations involve numbers that were not obtained using measuring devices but were determined by counting are significant.
Rounding off numbers
rounding
off
is when you reduce the number of decimal points in a number
Rules for rounding off
if the digit to be removed
b. if less than 5, the preceding digit stays the same.
a. if greater than or equal to five the preceding digit is increased by 1.
in a series of calculations you should carry a of the digits that show until the final number then round off using rule one.
when rounding off use only the first number to the right of the last significant figure.
Determining Significant Figures in Calculations
Rules for Using Significant Figures in Calculations.
for multiplication or division, the number of significant figures in the result is the same as that in the measurement with smallest number of significant figures.
this measurement is limiting because it limits the number of significant figures in the result.
multiplication and division, significant figures are counted.
for addition and subtraction the limiting term is the one with smallest number of decimal places.
for addition and subtraction the decimal places are counted.
Problem solving and dimensional analysis.
how do we convert from one unit to another
we use the formula Unit 1 x conversion factor = Unit 2
the
conversion factor
is a ratio of the two parts of the statement that relates the two units
conversion factors are ratios of the two parts of the equivalence statement.
we choose a conversion factor that cancels the unit we want to discard and leaves the units we want in the result
always think about if your answer makes sense.
an
equivalence statement
is when two measurements in different units are exactly the same amount.
Dimensional analysis
is changing from one unit to another via conversion factors.
converting from one unit to another
Step one use the equivalence statement that relates the two units
Step two choose the appropriate conversion factor by looking at the direction of the required change ( make sure the unwanted units cancel)
Step three multiply the quantity to be converted by the conversion factor to give the quantity with the desired units
Step four check that you have the correct number of significant figures
Step five ask whether your answer makes sense
Density
is the amount of matter present in a given volume of substance
Density is mass per unit volume,
the ratio is Density = Mass / Volume
much density is determined by how much water level changes when a person is momentarily submerged in it.
the more muscle and the less fat a person has, the higher his or her body density.
Density of substances
chloroform 1.483 g/cm 3
diethyl ether 0.714 g/cm 3
isopropyl alcohol isopropyl alcohol g/cm 3
toluene toluene g/cm 3
density can also be used to determine the amount of anitfreeze
specific gravity can beused to define density
Specific gravity
is defined as the ratio of the density of a given liquid to the density of water at 4 degrees C because it is a ratio of densities, specific gravity has no units
2.1 Scientific Notation
2.2 Units
2.3 Measurements of Length, Volume, and Mass
2.4 Uncertainty in Measurement
2.5 Significant Figures
2.6 Problem Solving and Dimensional Analysis
2.8 Density
