VII. Mathematics, Measurement, and Data Management; Laboratory Procedures and Safety.  There are 14 Questions

● Mathematics, measurement, and data manipulation

– Measurement and notation systems

– Data collection, manipulation, presentation and interpretation, including error analysis

● Laboratory procedures and safety

– Safe preparation, storage, use, and disposal of laboratory materials

– Use of appropriate laboratory procedures to prepare chemicals and materials

– Selection and use of appropriate laboratory equipment

– Emergency procedures for laboratory accidents

The U S System of Measurements

Length

12 inches                = 1 foot 

3 feet                      = 1 yard

5280 feet = 1 mile 

Volume

1728 cu. inches = 1 cubic foot

27 cu. feet               = 1 cubic yard

4 quarts                  = 1 gallon (8 pints)

Mass

Area

144 sq. inches  = 1 square foot

9 sq. feet     = 1 square yard

4840 sq. yards  = 1 acre

640 acres       = 1 square mile

1 sq.mile      = 1 section

36 sections    = 1 township

Volume

1728 cu. inches = 1 cubic foot

27 cu. feet   = 1 cubic yard

4 quarts    = 1 gallon (8 pints)

Mass

Category               Name      Abbrev.

Length                 metre        m

Mass                   kilogram     kg

Time                   second       s

Electric current       ampere       A

Temperature            kelvin       K

Amount of substance    mole         mol

1012     E 12     tera     T

109      E  9     giga     G

106      E  6     mega     M

103      E  3     kilo     k

102      E  2     hecto    h

101      E  1     deca     da

10-1     E -1     deci     d

10-2     E -2     centi    c

10-3     E -3     milli    m

10-6     E -6     micro    µ

10-9     E -9     nano     n

10-12    E-12     pico     p

Significant Figures Answers

1) 3.0800 - five significant figures. All the rules are illustrated by this problem. Rule one - the 3 and the 8. Rule Two - the zero between the 3 and 8. Rule three - the two trailing zeros after the 8.

2) 0.00418 - three significant figures: the 4, the 1, and the 8. This is a typical type of problem where the student errs by giving five significant figures as the answer.

3) 7.09 x 10¯⁵ - three significant figures. When a number is written in scientific notation, only significant figures are placed into the numerical portion. If this number were taken out of scientific notation, it would be 0.0000709.

4) 91,600 - three significant figures. The last two zeros are not considered to be significant (at least normally). Suppose you had information that showed the zero in the tens place to be significant. How would you show it to be different from the zero in the ones place, which is not significant? The answer is scientific notation. Here is how it would be written: 9.160 x 10⁴. This CLEARLY indicates the presence of four significant figures.

5) 0.003005- four significant figures. No matter how many zeros there are between two significant figures, all the zeros are to be considered significant. A number like 70.000001 would have 8 significant figures.

6) 3.200 x 10⁹ - four significant figures. Notice the use of scientific notation to indicate that there are two zeros which should be significant. If this number were to be written without scientific notation (3,200,000,000) the significance of those two zeros would be lost and you would - wrongly - say that there were only two significant figures.

7) 2

8) 2

9) 3

10) 3

Significant Figures in Calculations:

When multiplying, dividing, or taking roots, the result should have the same number of significant figures as the least precise number in the calculation (this is why the amount of the check in the example above should have only four significant figures)

When adding or subtracting, the absolute precision of the result cannot be greater than that of the least precise number in the calculation (thus, if you add 0.02g of NaCl to 243 g of water, the total mass should be expressed as 243g , not 243.01g, since the mass of water has the less precise absolute precision ( 1g vs. 0.01g))

If a calculation involves a combination of mathematical operations having different significant figures, it is customary practice to carry out the calculation using all figures, and then go back and figure out how many significant figures the final result should have.

SI DERIVED UNITS

Data Collection, manipulation, and interpretation

How to Construct a Line Graph on Paper

Graphs are a useful tool in science. The visual characteristics of a graph make trends in data easy to see. One of the most valuable uses for graphs is to "predict" data that is not measured on the graph.

• Extrapolate: extending the graph, along the same slope, above or below measured data.
• Interpolate: predicting data between two measured points on the graph.

What are variables. Variables are things that we measure, control, or manipulate in research. They differ in many respects, most notably in the role they are given in our research and in the type of measures that can be applied to them.

1. Independent Variable - controlled by people, the X axis.  Should be on the left of a data table.
2. Dependent Variable - changes with the independent variable--Y axis

The terms independent variable" and "dependent variable should be used only when referring to experimental research, where the independent variable is manipulated (ratio T cells vs. targeted cells) and the dependent variable is passively observed (percent lysis)

For example, if in an experiment, males are compared with females regarding their white cell count (WCC), Gender could be called the independent variable and WCC the dependent variable.

Making Science Graphs and Interpreting Data

Most scientific graphs are made as line graphs. There may be times when other types would be appropriate, but they are rare. The lines on scientific graphs are usually drawn either straight or curved. These "smoothed" lines do not have to touch all the data points, but they should at least get close to most of them. They are called best-fit lines.

x independent variable; y dependent variable