# 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

 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

## 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.

## LENGTH

 Millimeters (mm) Centimeters (cm) Inches (in) Feet (ft) Yards (yd) Meters (m) 1.0 0.1 0.03937 0.00328 0.0011 0.001 10.0 1.0 0.3937 0.03281 0.0109 0.01 25.4 2.54 1.0 0.0833 0.0278 0.0254 304.8 30.48 12.0 1.0 0.333 0.3048 914.40 91.44 36.0 3.0 1.0 0.9144 1000.0 100.0 39.37 3.2808 1.0936 1.0
• 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) 1.0 0.061 0.00106 0.001 3.697 0.226 0.00391 0.00369 16.3866 1.0 0.0173 0.01639 29.573 1.8047 0.03125 0.02957 946.332 57.75 1.0 0.9463 1000.0 61.025 1.0567 1.0
• 1 gallon = 4 quarts = 8 pints = 3.785 liters.
• 1 pint = 473.16 mL.

## WEIGHT

 Grains (gr) Grams (g) Apothecaries' Ounces (f℥) Kilograms (kg) 1.0 0.0648 0.00208 0.000065 15.432 1.0 0.03215 0.001 480.0 31.1 1.0 0.0311 7000.0 453.5924 14.583 0.45359 15432.358 1000.0 32.15 1.0
• 1 microgram (μg) = 0.001 milligram.
• 1 mg = 1 milligram = 0.001 g; 1000 mg = 1 g.

## CIRCULAR MEASURE

 60 seconds = 1 minute 60 minutes = 1 degree 90 degrees = 1 quadrant 4 quadrants = 360 degrees = circle

## LIQUID MEASURE

 16 ounces = 1 pint 4 quarts = 1 gallon 1 quart = 946.35 milliliters 1000 milliliters = 1 liter 31.5 gallons = 1 barrel (U.S.) 1 liter = 1.0566 quart 4 gills = 1 pint 2 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 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.

## PRESSURE

 TO OBTAIN MULTIPLY BY lb/sq in atmospheres 14.696 lb/sq in in of water 0.03609 lb/sq in ft of water 0.4335 lb/sq in in of mercury 0.4912 lb/sq in kg/sq meter 0.00142 lb/sq in kg/sq cm 14.22 lb/sq in cm of mercury 0.1934 lb/sq ft atmospheres 2116.8 lb/sq ft in of water 5.204 lb/sq ft ft of water 62.48 lb/sq ft in of mercury 70.727 lb/sq ft cm of mercury 27.845 lb/sq ft kg/sq meter 0.20482 lb/cu in g/mL 0.03613 lb/cu ft lb/cu in 1728.0 lb/cu ft gm/mL 62.428 lb/U.S. gal gm/L 8.345 in of water in of mercury 13.60 in of water cm of mercury 5.3543 ft of water atmospheres 33.95 ft of water lb/sq in 2.307 ft of water kg/sq meter 0.00328 ft of water in of mercury 1.133 ft of water cm of mercury 0.4461 atmospheres ft of water 0.02947 atmospheres in of mercury 0.03342 atmospheres kg/sq cm 0.9678 bars atmospheres 1.0133 in of mercury atmospheres 29.921 in of mercury lb/sq in 2.036 mm of mercury atmospheres 760.0 g/mL lb/cu in 27.68 g/sq cm kg/sq meter 0.1 kg/sq meter lb/sq in 703.1 kg/sq meter in of water 25.40 kg/sq meter in of mercury 345.32 kg/sq meter cm of mercury 135.95 kg/sq meter atmospheres 10332.0 kg/sq cm atmospheres 1.0332

## FLOW RATE

 TO OBTAIN MULTIPLY BY cu ft/hr cc/min 0.00212 cu ft/hr L/min 2.12 L/min cu ft/hr 0.472

## 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 −1.00 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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