MODULE A - 4

MEASUREMENT SYSTEMS & SCIENTIFIC NOTATION

OBJECTIVES

• At the end of this module, the student will be able to… Identify and compare the systems of

measurement used in the clinical setting. Identify the standard prefixes used in the metric

system State the metric units of length, mass, volume,

time, and temperature. Distinguish between the metric units for liquid

(mL) and solid volume (cc) measurements.

Measurement systems

• Method of quantifying matter Solids, liquids & gases

• Quantities include: Length Area Weight Volume Pressure Temperature Time

• Systems used in medicine:A. ConventionalB. MetricC. Standard International

Conventional Systems

• Also known as: British English U.S Customary (FPS) foot, pound, second(FPS) foot, pound, second

• Commonly used in U.S.

FPS

Examples of length & area

12 inches = 1 foot

3 feet (36 inches) = 1 yard

220 yards = 1 furlong

8 furlongs = 1 mile

1,760 yards = 1 mile

5,280 feet = 1 mile

1 sq. foot (foot2) = 122 sq. inches

1 sq. yard (yard2) = 9 sq. feet

43,560 sq. feet = 1 acre

1 sq. mile (mile2) = 640 acres

Examples of liquid measure

1 teaspoon (tsp) = 1/3 tablespoon

2 tablespoon (tbsp) = 1 fluid ounce

1 fluid ounce (oz) = 1/8 cup

2 fluid ounces = 1/4 cup

2 2/3 fluid ounces = 1/3 cup

4 fluid ounces = 1/2 cup

5 1/3 fluid ounces = 2/3 cup

6 fluid ounces = 3/4 cup

8 fluid ounces = 1 cup

2 cups (c) = 1 pint

2 liquid pints (pt) = 1 liquid quart (qt)

4 liquid pints = 1 gallon (gal)

Examples of dry measure

1 dry quart = 2 dry pints

8 dry pints = 1 peck

4 pecks = 1 bushel

Standard International (SI)

• Simplified modification of metric system.

• Worldwide effort started in 1960s to standardize to this system.

• Also known as: (MKS) meter, kilogram, second

MKS

Comparison

Conventional Units Standard International Units

Length inch or foot meter

Volume Fluid ounce

Cubic Foot (ft3)

Liter

Area in2 or ft2 m2

Metric System

• Developed in Europe.

• Has all units based on multiples of 10.

• Also known as: (CGS) centimeter, gram, second

CGS

Measurements in Respiratory Therapy• Length

Meter (m)

• Volume Liter (L)

• Mass Gram (g)

• Time Seconds (sec)

• Temperature Centigrade (Celsius), Kelvin, Fahrenheit

• Pressure Centimeters of Water (cm H2O), Pounds per square

inch (psi), Millimeters of mercury (mm Hg), Torr, Pascal (Pa), and Atmospheres (atm)

• Force Dynes

Conversion

• Conversion within the metric system is easy Everything based on multiples of ten.

• Conversion from one system to the other: MustMust know the conversion factors.

Conversion

• Conversion within these systems or from one system to the other: You Must know how to do metric conversions. I will provide the S.I. and conventional factors on

an exam or quiz.• There are too many to memorize.

• Gimli Glider & Mars Climate Orbiter

Basic (fundamental) Units

• Basic unit has value of one. (1x100 = 1) One Liter

• Smaller - milliliter

• Larger - kiloliter

One Gram• Smaller – microgram

• Larger - hectogram

One Meter• Smaller - decimeter

• Larger - Megameter Smaller

Larger

Opposite of the number line

Basic or Fundamental Unit

Liter

Gram

Meter

105 104 103 102 101 100 10-1 10-2 10-3 10-4 10-5

|-------|-------|-------|-------|-------|-------|-------|-------|------|-------|

kilo hecto deca deci centi milli

x1000 x100 x10

(k) (h) (da) (d) (c) (m)

LARGER SMALLER

Metric Chart

10

1

100

1

1000

1

Greek Prefixes - Units to the left of the basic unit and larger.• BASIC UNIT = One Liter, Gram or Meter

• 10 1 deca (da) 10 x larger 10

• 10 2 hecto (h) 100 x larger 100

• 10 3 kilo (k) 1000 x larger 1000

• 10 4

• 10 5

• 10 6 Mega (M) 1,000,000x 1,000,000

• 10 7

• 10 8

• 10 9 Giga (G) 1,000,000,000x 1,000,000,000

Latin Prefixes Units to the right of the basic unit and smaller.

• BASIC UNIT = One Liter, Gram or Meter

• 10 -1 deci (d); 10 x smaller; 1/10; x 0.1

• 10 -2 centi (c); 100 x smaller; 1/100; x 0.01

• 10 -3 milli (m); 1000 x smaller; 1/1,000; x 0.001

• 10 -4

• 10 -5

• 10 -6 micro () or (mc); 1,000,000 x smaller; 1/1,000,000; x 0.000001

• 10 -7

• 10 -8

• 10 -9 nano (n); 1,000,000,000 x smaller; 1/1,000,000,000; x 0.000000001

• 10-10 Angstrom (Å); 10,000,000,000 x smaller; 1/10,000,000,000; x 0.0000000001

Scientific Notation

• A method of expressing the value of a very small or very large number.

• Scientific Notation: (base exponent)

Base is the number to be multiplied by itself (usually 10).

Exponent is the number of times it is multiplied.

• 103 = 10 x 10 x 10 = 1,000

Scientific Notation

Example:

• A kilometer is 1,000 times larger than a meter

• Count the zeros (that equals exponent)

• 103

• 10x10x10 times larger

Scientific Notation

Example:• Angstrom (Å) is 10 billion times smaller than a meter

(m)• That is…10,000,000,000 times smaller• Count the zeros to determine exponent

or or

• Can also be written as 0.0000000001• 10x10x10x10x10x10x10x10x10x10 times smaller

1010

100000000010

1

,,,1010

Numbers and Exponents100= 1 a x 100 = a

101= 10 a x 101 = a x 10

102= 100 a x 102 = a x 100

103= 1000 a x 103 = a x 1000

106= 1,000,000 a x 106 = a x 1,000,000

109= 1,000,000,000 a x 109 = a x 1,000,000,000

10-1 = 0.1 a x 10-1 = a x 0.1

10-2 = 0.01 a x 10-2 = a x 0.01

10-3 = 0.001 a x 10-3 = a x 0.001

10-6 = 0.000001 a x 10-6 = a x 0.000001

10-9 = 0.000000001 a x 10-9 = a x 0.000000001

Numbers and Exponents

Positive exponent = # of zeros

5 x 100 = 5

5 x 101 = 50

5 x 102 = 500

5 x 103 = 5000

5 x 106 = 5,000,000

5 x 109 = 5,000,000,000

Negative exponent = # of decimal places

5 x 10-1 = 0.5

5 x 10-2 = 0.05

5 x 10-3 = 0.005

5 x 10-6 = 0.000005

5 x 10-9 = 0.000000005

Examples - Avogadro’s Number

Expresses the number of atoms in one mole of a gas

Long form:

602,000,000,000,000,000,000,000 atoms

Scientific notation:

6.02 x 10 23 atoms

Process: Count over to the left, the number of decimal places to get a number between 1 & 10

Example - Mass of an electron

Long Form:

0.000 000 000 000 000 000 000 000 000 000 911 grams

Scientific Notation:

9.11 x 10-31 grams

Process: Count over to the right the number of decimal places necessary to get a number between 1 and 10

Practice: Express the following exponentially

• 500 = 5 x 102

(count over to left 2 decimal places)

• 93,000,000 = _________________

• 0.0003 =_________________

• 0.000000024 = _________________

Exponent Relationship to Basic Unit

• Negative exponents are smaller (10 –3)

• Positive exponents are larger (10 3)

| | | | | |

If the metric system was money…

$1,000.00 $100.00 $10.00 $1.00 10 cent 1cent

Basic Unit

0.10 0.01

One more point regarding units

of measure.

Why is mL and cc (cm3) the same?

• Cubic centimeter (cc or cm3) and millimeter (mL) are used interchangeably in medicine. The unit cc is a length measurement. The unit mL is a volume measure.

• A cube 1 cm long x 1 cm wide by 1 cm high (l x w x h = area) will hold 1 mL of liquid volume.

• We therefore use the units interchangeably. 1 cc or cm3 = 1 mL

1 cm length

1 cm high

1 cm deep

Cubic centimeter

The volume of this cube

is one mL.

1 mL = 1 cc = 1 cm3

Additional Conversion Factors

Length:

1 meter = 39.37 inches

1 cm = .3937 inches

1 km = 0.62 miles

Volume:

1 mL = 1 cc = 1 cm3

1 L = 1.0567 qts.

946 mL = 1 qt.

1 pint = 473 mL

1 kg1 kg == 2.2 pounds (lbs)2.2 pounds (lbs)

1 lb = 454 grams