Units of Measurement (Including SI Units)

Scientific Notation

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

Now, dividing by 6,
= 1.234 × 10−2 × 1.2 = 1.4808 × 10−2 = 1.4808/100 = 0.014808

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

QuantityNameSymbol
Lengthmeterm
Masskilogramkg
Timeseconds
Electric currentampereA
TemperaturekelvinK
Luminous intensitycandelacd
Amount of a substancemolemol

SOME SI DERIVED UNITS

QuantityName of Derived UnitSymbol
Areasquare meterm2
Volumecubic meterm3
Speed, velocitymeter per secondm/s
Accelerationmeter per second squaredm/s2
Mass densitykilogram per cubic meterkg/m3
Concentration of a substancemole per cubic metermol/m3
Specific volumecubic meter per kilogramm3 /kg
Luminescencecandela per square metercd/m2
Body mass indexkilogram per meter squaredkg/m2

SI DERIVED UNITS WITH SPECIAL NAMES

QuantityNameSymbolExpressed in Terms of Other Units
FrequencyhertzHzs−1
ForcenewtonNkg·m·s−2 or kg·m/s2
PressurepascalPaN·m−2 or N/m2
Energy, work, amount of heatjouleJkg·m2· s−2 or N·m
PowerwattWJ·s or J/s
Quantity of electricitycoulombCA·s
Electromotive forcevoltVW/A
CapacitancefaradFC/V
Electrical resistanceohmΩV/a
ConductancesiemensSA/V
InductancehenryHWφ/A
Illuminanceluxlxln/m2
Absorbed (radiation) dosegrayGyJ/kg
Dose equivalent (radiation)sievertSvJ/kg
Activity (radiation)becquerelBqs−1

PREFIXES AND MULTIPLES USED IN SI

PrefixSymbolPowerMultiple or Portion of a Multiple
teraT10121,000,000,000,000.
gigaG1091,000,000,000.
megaM1061,000,000.
kilok1031,000.
hectoh102100.
decada10110.
unity1
decid10−10.1
centic10−20.01
millim10−30.001
microμ10−60.000001
nanon10−90.000000001
picop10 −120.000000000001
femtof10−150.000000000000001
attoa10−180.000000000000000001

Metric System

MASSES

MassGrams
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. 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.

LENGTH

Millimeters (mm)Centimeters (cm)Inches (in)Feet (ft)Yards (yd)Meters (m)
1.00.10.039370.003280.00110.001
10.01.00.39370.032810.01090.01
25.42.541.00.08330.02780.0254
304.830.4812.01.00.3330.3048
914.4091.4436.03.01.00.9144
1000.0100.039.373.28081.09361.0
  • 1 μm = 1 micrometer = 0.001 millimeter. 1 mm = 100 μm.
  • 1 km = 1 kilometer = 1000 meters = 0.62137 statute mile.
  • 1 statute mile = 5280 feet = 1.609 kilometers.
  • 1 nautical mile = 6076.042 feet = 1852.276 meters.

VOLUME (FLUID)

Milliliters (mL)Cubic Inches (in3 )U.S. Fluid Quarts (qt)Liters (L)
1.00.0610.001060.001
3.6970.2260.003910.00369
16.38661.00.01730.01639
29.5731.80470.031250.02957
946.33257.751.00.9463
1000.061.0251.05671.0
  • 1 gallon = 4 quarts = 8 pints = 3.785 liters.
  • 1 pint = 473.16 mL.

WEIGHT

Grains (gr)Grams (g)Apothecaries' Ounces (f℥)Kilograms (kg)
1.00.06480.002080.000065
15.4321.00.032150.001
480.031.11.00.0311
7000.0453.592414.5830.45359
15432.3581000.032.151.0
  • 1 microgram (μg) = 0.001 milligram.
  • 1 mg = 1 milligram = 0.001 g; 1000 mg = 1 g.

CIRCULAR MEASURE

60 seconds = 1 minute60 minutes = 1 degree
90 degrees = 1 quadrant4 quadrants = 360 degrees = circle

LIQUID MEASURE

16 ounces = 1 pint4 quarts = 1 gallon1 quart = 946.35 milliliters
1000 milliliters = 1 liter31.5 gallons = 1 barrel (U.S.)1 liter = 1.0566 quart
4 gills = 1 pint2 pints = 1 quart

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 centimeters40 rods = 1 furlong8 furlongs = 1 statute mile
12 inches = 1 foot3 feet = 1 yard5.5 yards = 1 rod
1 statute mile = 5280 feet3 statute miles = 1 statute league1 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 oz16 teaspoons (liquid) = 1 cup
3 teaspoons = 1 tablespoon12 tablespoons (dry) = 1 cup
1 tablespoon = ½ fl oz1 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 second1 minute = 1/60 of an hour
1 second = 1/60 of a minute1 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.

PRESSURE

TO OBTAINMULTIPLYBY
lb/sq inatmospheres14.696
lb/sq inin of water0.03609
lb/sq inft of water0.4335
lb/sq inin of mercury0.4912
lb/sq inkg/sq meter0.00142
lb/sq inkg/sq cm14.22
lb/sq incm of mercury0.1934
lb/sq ftatmospheres2116.8
lb/sq ftin of water5.204
lb/sq ftft of water62.48
lb/sq ftin of mercury70.727
lb/sq ftcm of mercury27.845
lb/sq ftkg/sq meter0.20482
lb/cu ing/mL0.03613
lb/cu ftlb/cu in1728.0
lb/cu ftgm/mL62.428
lb/U.S. galgm/L8.345
in of waterin of mercury13.60
in of watercm of mercury5.3543
ft of wateratmospheres33.95
ft of waterlb/sq in2.307
ft of waterkg/sq meter0.00328
ft of waterin of mercury1.133
ft of watercm of mercury0.4461
atmospheresft of water0.02947
atmospheresin of mercury0.03342
atmosphereskg/sq cm0.9678
barsatmospheres1.0133
in of mercuryatmospheres29.921
in of mercurylb/sq in2.036
mm of mercuryatmospheres760.0
g/mLlb/cu in27.68
g/sq cmkg/sq meter0.1
kg/sq meterlb/sq in703.1
kg/sq meterin of water25.40
kg/sq meterin of mercury345.32
kg/sq metercm of mercury135.95
kg/sq meteratmospheres10332.0
kg/sq cmatmospheres1.0332

FLOW RATE

TO OBTAINMULTIPLYBY
cu ft/hrcc/min0.00212
cu ft/hrL/min2.12
L/mincu ft/hr0.472

PARTS PER MILLION

Conversion of parts per million (ppm) to percent:
1 ppm = 0.0001%, 10 ppm = 0.001%, 100 ppm = 0.01%, 1000 ppm = 0.1%, 10,000 ppm = 1%, etc.

ENERGY

  • 1 foot pound = 1.35582 joule
  • 1 joule = 0.2389 Calorie (kilocalorie)
  • 1 Calorie (kilocalorie) = 1000 calories = 4184 joules
  • 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−1.00Litmus is red in this acid range
Gastric juice ‡ 1.4
Urine ‡ 6.0
Water7.00Neutral
Blood7.35-7.45Litmus is blue in this alkaline range.
Bile ‡ 7.5
Pancreatic juice8.5
Tenth-normal NaOH13.00
‡ 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.