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Math Used in Science

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Measurement

 

 

English Units of Measure and Equivalents

Length
1 foot (ft) = 12 inches (in)
1 yard (yd) = 3 ft
1 mile (mi) = 5280 ft
Volume
1 pint (pt) = 16 fluid ounces (fl oz)
1 quart (qt) = 2 pt
1 gallon (gal) = 4 qt

 
Weight
1 pound (lb) = 16 ounces(oz)
1 ton = 2000 lb
Time
1 minute (min) = 60 seconds (s)
1 hour (h) = 60 min
1 day = 24 h

 

The Metric System of Measurement
 

Length
1 centimeter (cm) = 10 millimeter (mm)
1 meter (m) = 100 cm
1 kilometer (km) = 1000 m
Weight
1 centigram (cg) = 10 milligram (mg)
1 gram (g) = 100 cg
1 kilogram (kg) = 1000 g

 
Volume
1 centiliter (cl) =

10 milliliter (ml)
1 liter (L) = 100 cl
1 kiloliter (kl) = 1000 L

 

         Prefix        decimal equivalent     exponential equivalent

 Pico            0.000000000001            10-12

 Nano              0.000000001             10-9

 Micro             0.000001                10-6

 Milli             0.001                   10-3

 Centi             0.01                    10-2

 Deci              0.1                     10-1

 no prefix         1.0                     100

 Deka             10.0                     101

 Hecto           100.0                     102

 Kilo           1000.0                     103

 Mega      1,000,000.                      106

 Giga  1,000,000,000.                      109

 

 

Scientific Notation

Scientists developed a method to make very large  and very small numbers more manageable using coefficients and exponents based on the powers of 10.

 

2,543,455,000 would be written 2.5 x 109

2.5 is the coefficient and  109 is the exponent or the power of 10.

 

Very small numbers would be written like this

0.00000000804 = 8.04 x 10-9

 

Scientific Notation

 

Significant Figures

Sig Figs

 

Dimensional Analysis

No naked numbers.... don't forget units!!!

Chemist picture

Convert 8.50 inches to cm

Discussion of Units Math Skill Review
  PowerPoint

 

Molecular Weight

•Molecular weight is the sum of the weights of all the atoms in a molecule.
•A mole (mol) is equal in number to the molecular weight of a substance, but upscaled from daltons to units of grams.
 

Use the periodic table to calculate to molecular weight of each atom, and then add the totals together to get the mass of the molecule.  Your answer should always contain the proper units, g/mol.

•One mole of sucrose weighs 342 g.

•C12H22O11
          •12 x  12 g  =  144 g/mol
•22 x   ___ = ___
•  11 x   ___ = ___
                   342 g/mol
 
1.0 M solution would have 342 g of sucrose to 1 liter of water

One mole of ethyl alcohol (C2H6O) also contains 6.022 x 1023 molecules but weighs only 46g because the molecules are smaller.

 

Calculating Percent

To find out what percent of one number is of another, divide the part by the whole.

 

What percent of 150 is 76?

P x 150 = 76

So, 76 is about 51% of 150

 

When working word problems, use the following:
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substitute "what percent" with the letter p, and solve for p

bullet

substitute "what number" with the letter n, and solve for n

bullet

of means times (x)

bullet

is means equals (=)

 

 

Graphing in Science

 

 

You are expected to graph in science to show your results.  Make sure you understand the basics of graphing line graphs, lines of best fit, scatter plots, and spread sheets. 

You will need to know the difference between the independent variable and dependent variable and label your graph properly.

 

 

Frequency Distribution

This relative frequency of a particular observation or class interval is found by dividing the frequency (f) by the number of observations (n): that is, (f ÷ n). Thus:

Relative frequency = frequency ÷ number of observations

The percentage frequency is found by multiplying each relative frequency value by 100. Thus:

Percentage frequency = relative frequency X 100 = f ÷ n X 100

 

Dependent and Independent Variables

Dependent Variable (DV)

A dependent variable is used synonymously with the term predictor variable. 

This variable is manipulated by the researcher, which in turn effects the independent variable. 

 

Independent Variable (IV)

An independent variable is also referred to as a criterion variable.  This particular variable is measured, predicted and monitored.  It is manipulated by the dependent variable in an experiment.

As you explore the natural and physical world and begin investigating  the cause and effect (correlations) between variables, it will become very clear there are common, frequently occurring mathematical relationships in science.

There are also moderating variables, extraneous variables, control variables, and intervening variables.

Independent Variable Dependent Variable
Predictor Criterion
Presumed cause Presumed effect
Stimulus Response
Predicted from ... Predicted to...
Antecedent Consequence
Manipulated Measured outcome

Cooper, et al. (2006). In Business research methods (p. 41). New York: McGraw-Hill/Irwin.

 

Temperature

Common temperatures to the nearest whole degree

 

Material Point

Kelvin

°Celsius

°Fahrenheit
copper m.p. 1356 1083 1981
gold melt pt 1336 1063 1945
aluminum m.p. 933 660 1219
lead melt pt 601 327 621
H2O bp1atm 373 100 212
chicken body 313 40 104
human body 310 37 98.6
room temp. 293 20 68
H2O m.p. 273 0 32
zero °F 292 -19 0
mercury m.p. 234 -39 -38
°C = °F 233 -40 -40
absolute zero 0 -273 -460

*Remember, there is no such thing as negative in the Kelvin scale or °K, it's just K.

Kelvin scale begins at absolute zero, (-273.15oC).

Absolute Zero is the coldest temperature, that means it's the temperature at which molecules (of any substance) have no more kinetic energy they can give up.

 

Converting Temperature Scales

 

•Celsius to Fahrenheit

•F= (9/5 x C) + 32

•Fahrenheit to Celsius

•C = 5/9(F-32)

•Celsius to Kelvin

•K = C+ 273

 

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