Sometimes it is necessary to use very large and very small numbers. These can best be indicated and handled in calculations by use of scientific notation, which is to say by use of exponents. Use of scientific notation requires writing the number so that it is the result of multiplying some whole number power of 10 by a number between 1 and 10. Examples are:
1234 = 1.234 × 103
0.01234 = 1.234 × 1/100 = 1.234 × 10−2
0.001234 = 1.234 × 1/1000 = 1.234 × 10−3
To convert a number to its equivalent in scientific notation:
Place the decimal point to the right of the first non-zero digit. This will now be a number between 1 and 9.
Multiply this number by a power of 10, the exponent of which is equal to the number of places the decimal point was moved. The exponent is positive if the decimal point was moved to the left, and negative if it was moved to the right. For example:
1,234,000.0 × 0.000072/6000.0 = 1.234 × 106× 7.2 × 10 −5/6.0 × 103
Now, by simply adding or subtracting the exponents of ten, and remembering that moving an exponent from the denominator of the fraction to the numerator changes its sign,
= 1.234 × 106 × 10 −5 × 10 −3 × 7.2/6 = 1.234 × 10−2 × 7.2/6
The last operation changed 1.4808 × 10−2 into the final value, 0.014808, which is not expressed in scientific notation.
SI Units (Système International d’Unités or International System of Units)
This system includes two types of units important in clinical medicine. The base units are shown in the first table, derived units in the second table, and derived units with special names in the third table.
SI BASE UNITS
Quantity
Name
Symbol
Length
meter
m
Mass
kilogram
kg
Time
second
s
Electric current
ampere
A
Temperature
kelvin
K
Luminous intensity
candela
cd
Amount of a substance
mole
mol
SOME SI DERIVED UNITS
Quantity
Name of Derived Unit
Symbol
Area
square meter
m2
Volume
cubic meter
m3
Speed, velocity
meter per second
m/s
Acceleration
meter per second squared
m/s2
Mass density
kilogram per cubic meter
kg/m3
Concentration of a substance
mole per cubic meter
mol/m3
Specific volume
cubic meter per kilogram
m3 /kg
Luminescence
candela per square meter
cd/m2
Body mass index
kilogram per meter squared
kg/m2
SI DERIVED UNITS WITH SPECIAL NAMES
Quantity
Name
Symbol
Expressed in Terms of Other Units
Frequency
hertz
Hz
s−1
Force
newton
N
kg·m·s−2 or kg·m/s2
Pressure
pascal
Pa
N·m−2 or N/m2
Energy, work, amount of heat
joule
J
kg·m2· s−2 or N·m
Power
watt
W
J·s or J/s
Quantity of electricity
coulomb
C
A·s
Electromotive force
volt
V
W/A
Capacitance
farad
F
C/V
Electrical resistance
ohm
Ω
V/a
Conductance
siemens
S
A/V
Inductance
henry
H
Wφ/A
Illuminance
lux
lx
ln/m2
Absorbed (radiation) dose
gray
Gy
J/kg
Dose equivalent (radiation)
sievert
Sv
J/kg
Activity (radiation)
becquerel
Bq
s−1
PREFIXES AND MULTIPLES USED IN SI
Prefix
Symbol
Power
Multiple or Portion of a Multiple
tera
T
1012
1,000,000,000,000.
giga
G
109
1,000,000,000.
mega
M
106
1,000,000.
kilo
k
103
1,000.
hecto
h
102
100.
deca
da
101
10.
unity
1
deci
d
10−1
0.1
centi
c
10−2
0.01
milli
m
10−3
0.001
micro
μ
10−6
0.000001
nano
n
10−9
0.000000001
pico
p
10 −12
0.000000000001
femto
f
10−15
0.000000000000001
atto
a
10−18
0.000000000000000001
Metric System
MASSES
Mass
Grams
1 Kilogram
=
1000.0
1 Hectogram
=
100.0
1 Decagram (Dekagram)
=
10.0
1 gram
=
1.0
1 decigram
=
0.1
1 centigram
=
0.01
1 milligram
=
0.001
1 microgram
=
10−6
1 nanogram
=
10−9
1 picogram
=
10−12
1 femtogram
=
10−15
1 attogram
=
10−18
Arabic numbers are used with masses and measures, as 10 g, or 3 ml. Portions of masses and measures are usually expressed decimally, e.g., 10−1 indicates 0.1; 10−6 = 0.000001. SEE: Appendix 7-1: Scientific Notation Appendix
.
Weights and Measures
Arabic numerals are used with masses and measures, as 10 g, or 3 mL. Portions of masses and measures are usually expressed decimally. For practical purposes, 1 cm3 (cubic centimeter) is equivalent to 1 mL (milliliter) and 1 drop (gtt.) of water is equivalent to a minim (m).
Note: Traditionally, the word “weights” is used in these tables, but “masses” is the correct term.
A U.S. gallon is equal to 0.8327 British gallon; therefore, a British gallon is equal to 1.201 U.S. gallons. 1 liter is equal to 1.0567 quarts.
LINEAR MEASURE
1 inch = 2.54 centimeters
40 rods = 1 furlong
8 furlongs = 1 statute mile
12 inches = 1 foot
3 feet = 1 yard
5.5 yards = 1 rod
1 statute mile = 5280 feet
3 statute miles = 1 statute league
1 nautical mile = 6076.042 feet
HOUSEHOLD MEASURES AND WEIGHTS†
Approximate Equivalents: 60 gtt. = 1 teaspoonful
= 5 ml = 60 minims = ⅛ ounce
1 teaspoon = ⅛ fl oz
16 teaspoons (liquid) = 1 cup
3 teaspoons = 1 tablespoon
12 tablespoons (dry) = 1 cup
1 tablespoon = ½ fl oz
1 cup = 8 fl oz
1 tumbler or glass = 8 fl oz; ½ pint
Conversion Rules and Factors
To convert units of one system into the other, multiply the number of units in column I by the equivalent factor opposite that unit in column II.
WEIGHT
1 gram
=
0.03527 avoirdupois ounce
1 gram
=
0.03215 apothecaries’ ounce
1 kilogram
=
35.274 avoirdupois ounces
1 kilogram
=
32.151 apothecaries’ ounces
1 kilogram
=
2.2046 avoirdupois pounds
1 grain
=
64.7989 milligrams
1 grain
=
0.0648 gram
1 avoirdupois ounce
=
28.3495 grams
1 apothecaries’ ounce
=
31.1035 grams
1 avoirdupois pound
=
453.5924 grams
VOLUME (AIR OR GAS)
1 cubic centimeter (cm3)
=
0.06102 cubic inch
1 cubic meter (m3)
=
35.314 cubic feet
1 cubic meter
=
1.3079 cubic yard
1 cubic inch (in3)
=
16.3872 cubic centimeters
1 cubic foot (ft3)
=
0.02832 cubic meter
CAPACITY (FLUID OR LIQUID)
1 liter
=
2.1134 pints
1 liter
=
1.0567 quart
1 liter
=
0.2642 gallon
1 fluid dram
=
3.697 milliliters
1 fluid ounce
=
29.573 milliliters
1 pint
=
473.1765 milliliters
1 quart
=
946.353 milliliters
1 gallon
=
3.785 liters
TIME
1 millisecond = one thousandth (0.001) of a second
1 minute = 1/60 of an hour
1 second = 1/60 of a minute
1 hour = 1/24 of a day
TEMPERATURE †
Given a temperature on the Fahrenheit scale, to convert it to degrees Celsius, subtract 32 and multiply by 5/9. Given a temperature on the Celsius scale, to convert it to degrees Fahrenheit, multiply by 9/5 and add 32. Degrees Celsius are equivalent to degrees Centigrade.
A large Calorie, or kilocalorie, is always written with a capital C.
pH
The pH scale is simply a series of numbers stating where a given solution would stand in a series of solutions arranged according to acidity or alkalinity. At one extreme (high pH) lies a highly alkaline solution; at the other extreme (low pH) is an acid solution containing 3.65 g of hydrogen chloride per liter of water. Halfway between lies purified water, which is neutral. All other solutions can be arranged on this scale, and their acidity or alkalinity can be stated by giving the numbers that indicate their relative positions. If the pH of a certain solution is 5.3, it falls between gastric juice and urine on the above scale, is moderately acid, and will turn litmus red.
Tenth-normal HCl
−1.00
Litmus is red in this acid range
Gastric juice
‡ 1.4
Urine
‡ 6.0
Water
7.00
Neutral
Blood
7.35-7.45
Litmus is blue in this alkaline range.
Bile
‡ 7.5
Pancreatic juice
8.5
Tenth-normal NaOH
13.00
‡ These body fluids vary rather widely in pH; typical figures have been used for simplicity. Urine samples obtained from healthy individuals may have pH readings anywhere between 4.7 and 8.0.
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