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Honors Unit 7 Study Guide
Measurements and Calculations
Scientific Method = A logical approach to solving problems that involves observing, collecting data, forming hypotheses, testing
these then forming theories based on the data.
Hypothesis = A testable statement.
Theory = A generalization that explains certain facts based on the work of many scientists.
Quantity = Something that has size/amount and can be measured. EX. volume
International System of Units (SI) = Metric system agreed on by scientists.
Base Units:
1. Length
2. Mass
3. Time
4. Temperature
5. Amount of substance
6. Electric Current
7. Luminous Intensity
Unit Name
meter (m)
kilogram (kg)
second (s)
Kelvin (K)
mole (mol)
ampere (A)
candela (cd)
Prefixes added to represent larger or smaller quantities.
Prefix
Meaning
abbreviation
Ex. Centic
Example
1/100
1 centigram =0.01 gram
1.
MegaM
1,000,000
1 Megaton = 106 ton
2.
Kilok
1,000
1 kilometer = 103 m
3.
Hectoh
100
1 hectometer = 100 m
4.
Dekada
10
1 dekaliter = 10 L
5.
Decid
1/10
1 decimeter = 0.1 m
6.
Centic
1/100
1 centimeter = 0.01m
7.
Millim
1/1,000
1 milligram = 0.001 g
8.
Micro
1/1,000,000
1 micrometer = 1 x 10-6 m
9.
Nanon
1/1,000,000,000
1 nanometer = 1 x 10-9m
10.
Picop
1/1,000,000,000,000
1 picogram = 1 x 10-12 g
Derived/Compound Units = Formed from a combination of the 7 base units.
Derived Unit
1. Area
2. Volume
3. Density
4. Molar Mass
5. Concentration
6. Molar Volume
7. Energy
8. Pressure
Formula
length x width
l x w x height
mass/volume
mass/amount substance
amount substance/volume
volume/amount substance
force x length
mass/length x time2
Unit Name
square meter (m2)
cubic meter (m3)*
kg/m 3 **
kg/mol
mol/L = M
m3/mol
joule (J)
kg/m x s2
*For volume we use a non SI unit since the m3 is large and cumbersome to use. We use cm3 or mL and … 1 cm3 = 1 ml.
** Density = A measure of how massive objects are compared to their size.
Use the Density triangle to calculate any one variable when you are given the other 2.
Ex. Diamond has a density of 3.26 g/cm3. What is the mass of a diamond with a volume of 0.350 cm3?
D = 3.26 g/cm3
v= 0.350cm3
D = m/v
= 3.26 g/cm3 X 0.350 cm3
= 1.14 g
Accuracy = Closeness of the measurement to the accepted/true/correct value of the quantity being measured.
Precision = Refers to the closeness of a set of multiple measurements to each other.
% Error = True/accepted value - Experimental value
True/accepted value
X 100
Significant Figures = The number of digits that are written down and are known with certainty plus one final digit that is
guessed/uncertain/estimated.
Digits are significant if:
1. The digit is not zero.
2. The zero is imbedded, between 2 nonzero digits.
3. Trailing zeros in a number that has a decimal point.
Digits ARE NOT significant if:
1. The zeros are to the left of all nonzero digits.
2. Trailing zeros in a number that does NOT have a decimal point.
Atlantic- Pacific Rule - This is a simple way to remember the above rules.
Follow these steps to figure out the number of sig.fig.s in a given number.
Step 1: If decimal is Present, start from the Pacific (left) side of the number
If decimal is Absent, start from the Atlantic (right) side of the number.
Step 2: Find the first non-zero digit in the number (1 -9) and start counting at this #.
Step 3: Continue counting the digits (0-9) in the # until you reach the opposite end of the #.
Ex. 4.0567 has 5 sig. fig.s and 102900 has 4 sig. fig.s.
Rounding Sig. Fig.s
Draw a line after the last sig. fig. to be kept.
If the digit to the right of the line is 5 or higher, round the last digit to be kept up by one.
If the digit to the right of the line is 4 or less, the last digit to be kept stays the same.
Ex. Round 42.68 to 3 sig. fig.s. The answer is 42.7
Round 17.32 to 3 sig. fig.s. The answer is 17.3
Addition & Subtraction with Sig. Fig.s
Your answer must have the same number of digits to the right of the decimal point as there are in the measurement being
added or subtracted having the fewest digits to the right of the decimal point.
Ex. 5.44g – 2.6103g = 2.83g
If there are no decimal points in one or more of the numbers, then the last digit kept should correspond to the first
uncertainty in that/those number(s). Zeros are used to hold place.
Ex. 534g + 2.6103g = 537 since the first uncertainty in the # without a decimal is the 4 in the “ones” place.
Multiplication & Division with Sig. Fig.s
Your answer cannot have more sig.fig.s than the number being multiplied or divided having the fewest number of sig.fig.s.
Ex. 2.4 g/mL X 15.82 mL = 38 g
Instrument Reading and Significant Figures:
It is generally accepted that scientific measurements can be estimated to one-tenth of the smallest mark on the instrument.
Therefore, if a ruler has markings every 1 centimeter, a person can reliably estimate to the nearest 0.1 cm, etc..
Scientific Notation = A method of representing very large and very small numbers using exponents.
M x 10n where
M is the coefficient and must be at least 1 and less than 10 and have the same # sig. fig.s as the number
itself does.
- 10n is the base 10 or power of 10 and n must be a whole #.
- When moving a decimal or changing an exponent, remember the following:
Each time you move a decimal to the:
Do this to the exponent:
Right
-1
Left
+1
Ex. 8 653 000 = 8.653 x 106
0.0037
= 3.7 x 10-3
Format:
Addition & Subtraction of # in Scientific Notation
Change n to make them the same power of 10 and move decimal place in M an equivalent number of decimal places.
When you move the decimal to the left decreasing M, you increase the power of 10; when you move the decimal to the right
increasing M, you decrease the power of 10.
Then add or subtract M ‘s and carry over power of 10.
Check that Sci. Not. is written so that M is at least 1 and less than 10.
Check original number using sig.fig. rules (look at fewest # places after decimal point).
Ex. 4.2 x 104 + 7.9 x 103 -----> 42. x 103 + 7.9 x 103 -----> 49.9 x 103 ----->
4.99 x 104 -----> 5.0 x 104
Multiplication of # in Scientific Notation
Multiply M’s then add exponents.
Check that Sci.Not. is written so that M is at least 1 and less than 10.
Check original numbers using sig. fig. rules (look at fewest # of sig.fig.s)
Ex. 5.23 x 106 m X 7.1 x 10-2m = 37.133 x 104 m2 = 3.7 x 105 m2
Division of # in Scientific Notation
Divide M’s then subtract exponents.
Check that Sci.Not. is written so that M is at least 1 and less than 10.
Check original numbers using sig.fig. rules (look at fewest # of sig.fig.s)
Ex. 5.44 x 107 g/8.1 x 104 mol = 0.671604 x 103 = 6.7 x 102 g/mol
Conversion Factor = A ratio derived from the equality between two different units that can be used to convert from one unit to
another.
(= to 1)
Ex. 3feet/ 1 yard
Dimensional Analysis/Factor-Label Method = A tool used in chemistry to set-up and solve problems.
Rules:
1. Whenever you write a number, include the units.
2. Numbers that are to be added or subtracted must have the same units. (If they’re not the same, convert before
adding/subtracting)
3. You can multiply and divide units whether or not they’re the same but whatever you do to the #’s you must also do the
same to the units.
4. When dividing compound units, invert the denominator and multiply.
5. Check the units after doing the math. If the units are not what you were looking for, there is a mistake, however,
correct units do not always mean you did the problem correctly.
The answer to a dimensional analysis problem showing the correct number of sig. fig.’s, should equal the number of sig.fig.s in
the original #.
EX. How many inches are in 2.31 miles?
Conversion factors: 12 inch = 1 foot 5280 ft = 1 mile
2.31 mile x 5280ft/1mile x 12 inch/1ft. = 146,000 inches
Directly proportional = A condition in which, as one value increases/decreases, so does another value increase/decrease at the
same rate.
- The result of dividing one value by another is a constant value.
All directly proportional relationships produce a straight line when graphed that passes through the origin.
Indirectly proportional = A condition in which, as one value increases, another value decreases and visa versa.
The product of multiplying one value by another is a constant value.
All indirectly proportional relationships produce a hyperbola when graphed.
Graphs = A diagram used to illustrate the relationship between two variables.
Have 2 axes: the x axis (abscissa) is horizontal and the y axis (ordinate) is vertical.
It is common to use the x axis as the independent variable which the scientist choses to vary and the y axis
as the dependent variable that is measured in response to the changes.
Most graphs are linear but some have curved lines.
In both cases the best smooth line is drawn through the plotted data points.
In very accurate work, a statistical analysis called the “method of least squares” is used to determine the
best straight line for the data. We will not learn this/do this but we will draw our best fit line through as
many points as possible keeping equal number of points that miss the line above it as are below it.
Determination of points between known data points is called interpolation and is more accurate then
determination of points beyond known data points which is called extrapolation.
The slope of a line is often needed as an experimental result.
It is calculated using the following formula where x and y are the coordinates of two data points:
y2 – y1
Slope =
x2 – x1