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Units of MeasurementSI units (Systeme Internationale d’Unites) were developed so that scientists could duplicate and communicate their work.
Base Units Derived Units
Length meter (m) Volume meter cubed (m3)
Mass kilogram (kg) Densitygrams per cubic
centimeter (g/cm3)
Time second (s)
Temperature kelvin (K)
A unit that is defined by a combination of a base units.
Density
Ratio of an object’s mass to its volume
What happens to density when mass is constant and volume changes?
Volume
massDensity
Volume
massDensity
Reliability of Measurements
Accuracy vs. PrecisionHow close a measured value is to an accepted value
How close a series of measurements are to one another
High AccuracyLow AccuracyHigh Accuracy
High Precision
Low Accuracy High Precision
Percent Error
Used to evaluate the accuracy of experimental data.
alValueExperimentlueAcceptedVaError
100xlueAcceptedVa
ErrororPercentErr
Pre-Class Activity
602000000000000000000000
What is the significance of this number?
How would you express this number in scientific notation?
Scientific Notation
6.02 x 1023CoefficientExponent
The coefficient must be greater than or equal to one and less than 10.
When expressing numbers less than one (ex. 0.001) in scientific notation, the decimal point is moved to the right until the coefficient is within range. The number of spaces moved is used to determine the exponent.
For numbers less than one, the exponent is negative
When expressing numbers greater than 10 (ex. 1000) in scientific notation, the decimal point is moved to the left until the coefficient is within range. The number of spaces moved is used to determine the exponent.
For numbers greater than 1, the exponent is positive.
Scientific Notation CalculationsMultiplication and Division For multiplication, multiply the coefficients and add the exponents
(1.3 x 104) x (2.0 x 106) =
Remember, your final answer must be in the correct form. Often, multiplication of coefficients will yield a number greater than 10. In this case the result must be changed into the proper form.
(5.3 x 104) x (2.0 x 106) = =
For division, divide the coefficients and subtract the exponents. Often, division of coefficients will result in a value that is less than one. If this occurs, the final result must be changed into the proper form.
(2.0 x 10-3) (4.00 x 104) = =
2.6 x 1010
10.6 x 1010 1.06 x 1011
0.5 x 10-7 5 x 10-8
Scientific Notation Calculations
Addition and Subtraction In order to add or subtract numbers in scientific notation, the
exponents of each number has to be the same As a rule of thumb, it is best to take the number with the lower
exponent and change it match the higher exponent. To increase an exponent, move the decimal point in the coefficient
to left, the number of spaces equal to the increase in the exponent. Once the exponents are equal, the coefficients can be added or
subtracted
2.1 x 104
+ 1 x 103
2.1 x 104
+ 0.1 x 104
2.2 x 104
5.37 x 10-4
- 6.2 x 10-5
5.37 x 10-4
- 0.62 x 10-4
4.75 x 10-4
Significant Figures in Measurement
Scientists determine the precision of instruments by the number of digits they report.
Significant Figures in Measurement
Measurements always include all certain digits and one uncertain digit.
52.7 mL
Measurement Challenge
What value would you assign to each of these measurements?
_________ mL
_________ cm
Identifying Significant Figures in Numbers
When examining a number, you determine the number of digits that are significant by the following rules:
1.All non-zero numbers are significant2.All final zeros to the right of a decimal are significant3.Zeros between significant digits are significant4.For positive numbers less than one, all zeros directly after
the decimal before the first significant figure are not significant.
5.All zeros at the end of a whole number are not significant.6.All contants and counting numbers have an unlimited
number of significant figures.
4.
5.
Sig Fig Challenge
How many sig figs are there in the following numbers:
1. 0.00042. 6873. 1.00824. 3305. 70.2080
Sig Fig Rules for Calculations
Multiplication and DivisionYour answer can not contain more or less sig figs than the operator that contains the least number of sig figs.
3.86 x 0.45=1.737 1.7
1.737Identify the significant figures, look on place beyond. If that digit is 5 or above, round up. If it is less than 5 drop off.
Sig Fig Rules for Calculations
Addition and Subtraction
Your answer can not be more precise than the least precise operator. Most of the time this means that your answer must have the same number of decimal places as the least precise operator
12.38 cm
+2.5 cm
14.88 cm 14.9 cm
1060 cm
+ 23.5 cm
1083.5 cm 1080 cm
If one of the numbers is a whole number that ends in zero(s), then the final answer must be rounded to the lowest place that contains a nonzero number.
Metric Conversions
mcdbdahK Move the decimal to the right
Move the decimal to the left
o Every metric unit is different from its neighbor by a factor of ten
o When converting between two units the decimal point is moved the number of places equal to the distance between the two unit in the chart above and in the same direction of movement
Sample problem
Convert the following 53 hg = ________dg
Start with 53.
Move the decimal 3 spaces to the right 53Fill in the empty spaces with zeros 53000 dg
mcdbdahK Move the decimal to the right
Move the decimal to the left
Sample Problem
Convert the following 300 cg = ________kg
Start with 300.
Move the decimal 5 spaces to the left 300Fill in the empty spaces with zeros 0.00300 kg
mcdbdahK Move the decimal to the right
Move the decimal to the left
More Practice Problems
Convert the following
0.058 dam = _______ dm
0.25 cL = _______ L
109 hg = ________ mg
mcdbdahK
5.8
0.0025
10900000
Factor Label Method of Conversion
Use conversion factors to systematically move from one unit to the next, cancelling out units on the diagonal in each step.
Convert 18 m = _______ cm
100 cm = 1 m 1 m = 100 cm 11
100
m
cm1
100
1
cm
m
18m100 cm
1 m= 1800 cm
Multistep Factor Label Problems
Convert
350 tsp = ______ L
Using the following conversion factors
1 tsp = 5 mL
1 L = 1000 mL
350 tsp 5 mL
1 tsp
1 L1000 mL
= 1.75 L
Multistep Factor Label Practice
Convert 3 min= ______ms
Use 1 min=60 s and 1000 ms = 1 s
Convert 32oz = _____ g
Use 16 oz=1 lb, 2.2 lb = 1kg, 1kg=1000 g
Multidimensional Factor Label Problems
Convert 25 g/mL = ______ kg/dL• Convert one unit at a time• Recognize that one unit is in the denominator
25 g
1 mL
1 Kg
1000 g
100mL
1 dL=2.5kg/dL
Multidimensional Factor Label Practice
Convert 85 km/hr = _________m/s
Convert 0.6 L/min = ________ qt/hrUse 1qt = 1.1L
Factor Label Practice for Area and Volume
1 ft = 12in
Remember to square or cube the unit as well as the number when converting to a squared or cubed unit
Graphing continued
Line Graphs In science, we draw a best fit line between data points.
Do not connect the dots.
Dep
ende
nt V
aria
ble
Dep
ende
nt V
aria
ble
Independent Variable Independent Variable
Which graph shows and indirect relationship between the dependent and independent variable?