Metric System:

• Any numerical measurement has a unit attached to it--what is a "unit"? A "unit" is a descriptor which indicates what the number means--length, mass, volume, or some combination thereof.
• The metric system is what is used primarily in science as numerical descriptors--there is only one other country in the world that is not metric besides the US -- Liberia.
• Metric distances are used in biology in microscopic distances -- µm -- scales on microscopes vary according to magnification and you will have to calibrate the scale you wish to use in order to measure cell sizes in your biology labs. Metric volumes and masses are used in medicine to determine the volume of medication that should be given to a patient of a particular body weight.
• All relationships in the metric system are based on multiples of ten relative to the basic unit:

• Some units are "derived" units or units which are a combination of other basic units-- some examples are volume and density.

Scientific/Exponential Notation: 

In the sciences we use scientific notation in order to express most numbers, especially those that are particularly large or small.

• There are two parts to a number written in exponential notation:
• a non-zero number (such as 100)
• times a ten to some exponential (whole) number power (such as 10 ², which is ten multiplied by itself two times)
  eg. exponential notation 100 x 10² = 100 x 10 x 10 = 10,000
  
• In scientific notation, the non-zero number is always a number between 1 and 10
• eg. scientific notation 1.00 x 10 ⁴ kg = 1.00 x 10,000 = 10,000 kg
  
• eg. scientific notation 2.203 x 10 ² cm = 2.203 x 100 = 220.3 cm
  
• eg. scientific notation 1.00 x 10 ^{- 4} m = 1.00 x 1/10,000 = 0.000100 m
  
• When converting numbers to scientific notation:
• if the number is greater than one, the exponent increases one unit (from zero) for every place the decimal is moved left to attain the non-zero number between 1 and 10.
• if the number is less than one, the exponent decreases one unit (from zero) for every place the decimal is moved right to attain the non-zero number between 1 and 10.
• eg. 0.00000000567 cm is 5.67 x 10 ^{- 9} cm decimal moved 9 places right
• eg. 1,230,000,000 m is 1.23 x 10 ⁹ m decimal moved 9 places left

Units:

SI units (le Système International) are the units from which all others are derived and is based on the metric system (as opposed to the English system):

• length is the meter (m)
• the meter is about 39 inches
• centimeter is 1/100 of a meter or 0.01 m or 1 x 10 ^{- 2} m
• mass is the kilogram (kg)
• a kg = kilogram = 1000 x gram
• time is the second (s)
• temperature is kelvin (K)
• amount of substance is the mole (mol)

Volume is not a basic unit, it is a unit derived from length -- width x depth x height

1 Liter (L) = 1 cubic decimeter (dm³) = 1 dm x 1 dm x 1 dm

1 L = 1000 mL = 1000 cm³ = 10 cm x 10 cm x 10 cm (1 dm = 10 cm)

Mass/Weight:

There is a distinction between mass and weight--in chemistry we always use mass

• mass
• quantity of matter
• weight
• the gravitational pull on that matter

Density is defined as the ratio of the mass of a substance to its volume and has units of mass/volume or g/cm³ or g/mL or kg/L.   For example, lead has a density of 11.3 g/cm³ or, put another way, 1 cm³ lead = 11.3 g lead.

Temperature and Heat:

Temperature reflects the hotness of a substance while heat is actually a form of energy.

Three different scales are used to measure temperature (Celsius or Kelvin is used predominantly in chemistry):

• Celsius or Centigrade Scale
  
• Kelvin or Absolute Scale
• absolute zero on kelvin scale represents the lowest possible temperature
• K = ° C + 273 or ° C = K - 273
  
• Fahrenheit ° F = 1.8° C + 32     or       ° C = ° F - 32
                                                                                 1.8

Significant Digits:

All numbers which represent a measurement must reflect the accuracy of that measurement which depends upon how the measurement was taken or what type of instrument was used.

• each device for taking a measurement has an inherent accuracy
• each number representing a measurement must represent that accuracy through significant digits

• The two rulers above have an inherently different accuracy in their ability to measure a length. The ruler with the greater number of delineation marks has a greater accuracy and, hence, can be read more exactly as indicated by the increased number of significant digits. Notice that the last significant digit is always an estimated digit, it cannot be read exactly, but can be reasonably estimated.

Rules: the underlined numbers are significant

• all non-zero digits are significant 2.346
• zeros between non-zero digits are significant 3.004
• zeros to the left of the first non-zero digit in a number are not significant 0.034
• when a number ends in zeros to the right of decimal point, the zeros are significant
  2.300
• when a number ends in zeros which are to the left of the decimal those zeros may or may not be significant 2000   or   2000   or   2000   or   2000

To determine the number of significant digits after a math operation:

• Multiplication/Division:
• The answer can contain no more total significant digits than the number of total significant digits contained in the data with the least number of significant digits.
• For example, in the multiplication below, one data has 3 significant digits, the other has 2 significant digits. The answer can have no more than 2 significant digits.
  
  (1.27)(2.3) = 2.921 = 2.9
  
• Addition/Subtraction:
• The answer can contain no more significant decimal digits than the number of significant decimal digits contained in the data with the least number of significant decimal digits.
• For example, in the addition below, one data has 1 significant decimal digit, one has 2 significant decimal digits, the third data has 3 significant decimal digits. The answer can have no more than 1 significant decimal digits (it does not matter how many total digits, only the decimal digits are important in addition and subtraction).
  
  1.0 + 2.15 + 3.468 = 6.618 = 6.6
   

Rounding Off:

 Rounding off is the method used to eliminate non-significant digits from the result of a calculation. The rules for rounding off are as follows:

• if the first digit to be dropped is less than 5, leave the preceding digit as it is
  1.8432 Û 1.8
• if the first digit to be dropped is 5 or greater, increase the preceding digit by 1
  1.8532 Û 1.9
  

Dimensional Analysis:

The use of dimensional analysis is very important in scientific calculations and conversion between different units, for example: 

Sample Calculations and Conversions:

• Convert the volume of a 10 m x 10 m x 10 m room to liters.
• To convert 1000 m³ to liters, we need conversion factors
  1 dm³ = 1 L             1 dm = 0.10 m
  
  
• 1000 m³   x    1 dm    x     1 dm    x     1 dm      =          1.0 x 10 ⁶ dm³
                        0.10 m         0.10 m       0.10 m
  
  cubic meters is cancelled, leaving cubic dm, by multiplying by the correct fraction or conversion factor
  
• 1.0 x 10 ⁶ dm³    x      1 L      =      1.0 x 10 ⁶ L
                                      1 dm³
  
  
• What is the mass of a piece of lead that has a volume of 10 cm³ and a density or 11.3 g/cm³?
• Density can be used as a conversion factor to convert between mass and volume.
  
• 10.0 cm³   x      11.3 g lead     =        113 g lead
                              1 cm³ lead
  
  
• Convert body temperature, 98.6 °F, to centigrade.
• We need a conversion formula: ° C = ° F - 32
                                                                       1.8
• °C = 98.6°F - 32    =     37 °C
                  1.8
  
  
• The boiling point of liquid nitrogen is 77K. Will nitrogen be a liquid or a gas at  -100°C?
• Another way of stating this question is, what is 77K in °C?
• We need a conversion formula: °C = K - 273
• °C = 77 K - 273
  °C = - 196 °C
• If the boiling point is –196 °C, then nitrogen must be a gas at -100 °C.
  
• If a tennis ball is served at 140 mph, what is its speed in m/s?
• We must convert mi to m so we need conversion factors for mi to m and h to s
                                h        s
  
• 1,609.4 m  &     3600 s
     1 mi                  1 h     
    
• 140 mi     x     1,609.4 m     x      1 h         =     62.6 m 
      1 h                   1 mi                 3600 s                   s  
    
  
  
• A cookbook calls for 600 mL of milk. How many cups does it call for?
• 1 mL    =      0.0338 oz                1 c   =    8 oz
  
• 600 mL       x        0.0338 oz       x      1 c       =       2.54 cups of milk
                                   1 mL                    8 oz
  
  
• Convert from 3.6 m to millimeters.
• 1 mm = 0.0010 m      or        1000 mm = 1 m
  
• 3.6 m     x        1000 mm       =        3.6 x 10 ³ mm
                               1 m