Chapter 5 - Measurements and Calculations
Chapter 5 - Measurements and Calculations
Measurement - quantitative observation - numerical
Qualitative observation – observation or description
Scientific Notation - expresses a number as a product of a
number between 1 and 10 and the appropriate power of ten
320 = 3.2 x 1020.0005 = 5 x 10-4400 000 = 4 x 105
If 5200 = 5.2 x 1000 then in scientific notation it equals 5.2 x
103.
1000 = 10 x 10 x 10 = 103
If 0.00025 = 2.5 x 0.0001 then in scientific notation it equals
2.5 x 10-4.
0.0001 = 0.1 x 0.1 x 0.1 x 0.1 = 10-4
(Negative exponents represent a fraction/reciprocal.)
Unit – tells which scale or standard is being used to represent
a measurement
· International System or SI system - based on metric system
· Length - measures distance - meter (m)
· Volume – three dimensional space occupied by a substance -
liter (L)
· Mass - quantity of matter present in an object - gram (g)
· Prefixes can be added to the base unit to represent size of a
quantity
Kilo- (k)1000 m = 1 km
Hecto- (h) 100 m= 1 hm
Deca- (D) 10 m=1 Dm
Base 1 m, L, g =1 m, L, g Substitute any base
Deci- (d) 1 m = 10 dmunit in for m
Centi- (c) 1 m =100 cm
Milli- (m) 1 m = 1000 mm
Uncertainty in Measurements – when making a measurement, record
all certain numbers plus one uncertain number. Measurements always
have some degree of uncertainty.
Accuracy – how close a measured value is to an accepted
value
Precision – how close a series of measurements are to one
another
Error – difference between an experimental value and an accepted
value
% error = |experimental value – accepted value| x 100%
accepted value
Significant Figures - (sig figs, SF) all certain numbers plus
first uncertain numbers.
We will be using this method of accounting and representing the
amount of uncertainty in any measurement or calculation.
Rules for Counting Significant Figures:
1.) All non-zero numbers are automatically significant 1-9.
2.) Zero’s fall into three categories.
a) Leading Zero’s- preceding all non-zero digits NEVER
COUNT!0.000213 = 3 SF
0.25 = 2 SF
b) Trapped Zero’s- fall between 2 non-zero digits ALWAYS
COUNT!20202 = 5 SF
40.05 = 4 SF
c) Trailing Zero’s- to the right of non-zero numbersonly count
IF there is a DECIMAL POINT.
3000 = 1 SF The lack of a decimal point shows the 3 is
estimated.
3000. = 4 SF The decimal shows that the last zero is an
estimated value.
4.0 = 2SF
3.) Infinite significant figures can occur with certain
quantities:
a) Definitions 1 m = 100 cm as well as 1 inch = 2.54 cm
b) Constants is but not 3.14 because it is an estimate
c) Counted Objects8 slices on pizza, 35 pennies
Rules for Rounding – If the digit to be removed is less than 5,
then the number stays the same. If the digit to be removed is equal
or greater than 5, then the number rounds up by one.
Multiplication and Division with Significant Figures
Number of significant figures is the result of the measurement
with the smallest number of significant figures.
4.638.46
x 7.5 2.1
Addition and Subtraction with Significant Figures
· Align the decimal points and carry out the calculation.
· First column to the right of the decimal with an uncertain
number determines the answer.
6.3416.791
.789 - 2.41__
+ 4.2__
Multiplication and Division with Scientific Notation and
Significant Figures
Multiplication Division
Multiply the NumbersDivide the Numbers
Add the ExponentsSubtract the Exponents
Multiply the UnitsDivide the Units
Round the Sig.FigsRound the Sig.Figs.
Example:(3.0 x 103 m) x (2.00 x 102 m)
Addition and Subtraction with Scientific Notation and
Significant Figures
· Must be to the same power of 10 and the same units so convert
to larger exponent (left)
· Perform addition or subtract and round to Sig.Figs.
· Units and exponents stay the same.
Example: (2.3 x 105 m) + (2.20 x 104 m)
Dimensional Analysis
Conversion factor- ratio of two parts of the statement that
relates the two units
All units will divide out except the unit being converted to in
the equivalence statement.
_______ km = 250 m
3.54 g = _____ mg
_____ mL = .542 kL
