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Math Made Meaningful
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Appendix
B
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Appendix B. Unit Conversions
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B.1
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Examples of US Units
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Abbrev.
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Name
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Derivation
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Illustrative Examples
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Length Dimension
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in
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inch
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between two knuckles of an average finger
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ft
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foot
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12 in
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average man's
foot
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yd
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yard
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3 ft
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from floor to
standard door knob
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mi
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mile
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5280 ft
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four times
around a traditional track field
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Weight Dimension
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oz
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ounce
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one-fourth cube
of butter
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lb
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pounds
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16 oz
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four cubes of
butter
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ton
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tons
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2000 ton
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a lot of butter
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Area Dimension
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in2
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square inch
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square that
surrounds a quarter
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ft2
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square feet
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144 in2
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average size of
floor tile
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yd2
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square yard
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9 ft2
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an average card
table
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acre
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acre
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4840 yd2
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just over 90
yards of a football field
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section
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section
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640 acres
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1 square mile
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township
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township
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36 sections
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6 miles by 6
miles
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Volume Dimension
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tsp
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teaspoon
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standard spoon
size
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tbsp
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tablespoon
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3 tsp
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large spoon size
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floz
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fluid ounce
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6 tsp
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2 large spoon
sizes
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cup
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cup
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8 floz
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small size
carton of milk
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pt
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pint
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2 cup
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standard size of
carton for cream
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qt
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quart
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2 pt
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medium size of
carton for milk
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gal
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gallon
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4 qt
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large size of
carton for milk
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B.2
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Examples of Metric Units
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Abbrev.
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Name
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Derivation
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Illustrative Examples
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Length Dimension
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mm
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meter
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width of one dime
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cm
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centimeter
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10 mm
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width of ten
dimes
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m
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meter
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10 cm
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one half height
of 6 foot 6 in basketball player
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km
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kilometer
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10 m
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almost three
times around high school track field
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Weight Dimension
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mg
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milligram
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g
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gram
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1000 mg
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water in small
thumbnail (1 ml)
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kg
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kilogram
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1000 g
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water in a
common size of bottled water (1 liter)
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tonne
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metric ton
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1000 kg
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water in a cubic
meter container
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Area Dimension
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mm2
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square
millimeter
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size of surface
of a pin head
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cm2
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square
centimeter
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100 mm2
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size of a small
fingernail
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dm2
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square
deciimeter
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100 cm2
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size of a small
fingernail
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m2
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square meter
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100 dm2
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just larger than
an average card table
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km2
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square kilometer
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1,000,000 m2
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about one third
of a square mile
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barn
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barn
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10-28 m2
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cross section of nuclei of atom
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Volume Dimension
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mL
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milliliter
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1 cm3
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small thumbnail
of water
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L
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liter
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1000 mL
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common size of
bottled water
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B.3
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Unit Prefixes
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Name
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Prefix
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Unit Identity
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Inverse Unit Identity
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yotta
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Y
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10^24 m/Ym
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10^-24 Ym/m
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zetta
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Z
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10^21 m/Zm
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10^-21 Zm/m
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exa
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E
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10^18 m/Em
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10^-18 Em/m
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peta
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P
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10^15 m/Pm
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10^-15 Pm/m
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tera
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T
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10^12 m/Tm
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10^-12 Tm/m
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giga
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G
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10^9 m/Gm
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10^-9 Gm/m
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mega
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M
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10^6 m/Mm
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10^-6 Mm/m
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kilo
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k
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10^3 m/km
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10^-3 km/m
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hecto
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h
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100 m/hm
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.01 hm/m
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deca
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da
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10 m/dam
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.1 dam/m
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1
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deci
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d
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0.1 m/dm
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10 dm/m
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centi
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c
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0.01 m/cm
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100 cm/m
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milli
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m
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10^-3 m/mm
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10^3 mm/m
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micro
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µ
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10^-6 m/µm
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10^6 µm/m
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nano
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n
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10^-9 m/nm
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10^9 nm/m
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pico
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p
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10^-12 m/pm
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10^12 pm/m
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femto
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f
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10^-15 m/fm
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10^15 fm/m
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atto
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a
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10^-18 m/am
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10^18 am/m
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zepto
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z
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10^-21 m/zm
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10^21 zm/m
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yocto
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y
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10^-24 m/ym |
10^24 ym/m |
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Unit Prefixes
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Since the metric system is conveniently based on the
decimal system, we can use prefixes to create units related to a given unit
by factors of ten. For example, a
kilogram (using the prefix "kilo") is a new unit derived from the
unit gram by multiplying by 1000. The
above table gives the unit identities that convert between such units.
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B.4
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System International (SI) Units
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The System International (SI) units provides the scientific community with
a consistent system of units in which to describe practically all known
physical phenomena. It begins with 7
base units (and two angle units) upon which all other units are derived.
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Abbreviation
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Unit
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Dimension
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SEVEN
BASE UNITS
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m
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meter
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length
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kg
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kilogram
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mass
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s
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second
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time
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A
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ampere
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electric current
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K
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kelvin
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temperature
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mol
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mole
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amount of matter
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cd
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candela
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luminous intensity
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ANGLE
UNITS
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rad
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radians
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plane angle
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sr
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steradians
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solid angle
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DERIVED
UNITS
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m2
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meters squared
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area
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m3
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meters cubed
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volume
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m/s
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meters per second
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velocity
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m/s2
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meters per second squared
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acceleration
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rad/s
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radians per second
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angular velocity
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rad/s2
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radians per second squared
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angular acceleration
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kg/m3
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kilograms per meters cubed
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density
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cd/m2
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candela per meter squared
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luminance
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A/m
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ampere per meter
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magnetic field strength
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DERIVED
UNITS
WITH NEW
SYMBOLS
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N = kg*m/s2
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newton
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force
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Pa = N/m2
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pascal
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pressure
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J = N*m
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joule
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quantity of energy
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W = J/s
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watt
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power
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V = W/A
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volt
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voltage
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ohm
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electric resistance
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C = A*s
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coulomb
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electric charge
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F = C/V
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farad
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electric capacitance
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Hz = cycles/s
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hertz
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frequency
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Wb = V*s
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weber
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magnetic flux
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T = Wb/m2
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tesla
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magnetic flux density
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H = Wb/A
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henry
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inductance
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lm = cd*sr
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lumen
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flux of light
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lx = lm/m2
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lux
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illumination
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SI Units
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B.5
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Conversions between US and Metric Units
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US Unit
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Metric Unit
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Dimensions
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1 in
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= .0254 m
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Length
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1 ft
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= .3048 m
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Length
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1 yard
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= .9144 m
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Length
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1 mile
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= 1,609 m
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Length
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1 angstrom
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= 10-10 m
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Length (electromagnetic waves)
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1 light-year
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= 9.461 x 1015
m
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Length (galaxies)
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1 ounce
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= .0283 kg
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Mass
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1 pound
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= .453 kg
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Mass
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1 ton
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= 906 kg
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Mass (2000 lb)
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1 tonne
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= 1,000 kg
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Mass (metric tone)
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1 minute
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= 60 sec
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Time
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1 hour
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= 3,600 sec
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Time
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1 day
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= 86,400 sec
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Time
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1 year
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= 3.15 x 107
sec
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Time
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1 acre
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= 4,047 m2
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Area
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1 hectare
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= 10,000 m2
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Area
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1 barn
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= 10-28
m2
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Area (cross section of nuclei)
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1 liter
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= .001 m3
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Volume
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1 gallon
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= .00378 m3
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Volume
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1 quart
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= .000946 m3
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Volume
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1 pint
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= .000473 m3
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Volume
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1 cup
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= .000236 m3
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Volume
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1 mph
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= .445 m/sec
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Velocity
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1 kph
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= 1,000 m/sec
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Velocity
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1 dyne
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= 10-5
newton
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Force
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1 erg
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= 107
joule
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Energy
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1 cal
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= 4.1869 joule
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Energy (calorie)
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1 Btu
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= 1,055 joule
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Energy (British thermal units)
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1 kWh
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= 3.6 x 106
joule
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Energy (kilowatt-hours)
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1 eV
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= 1.6 x 10-19
joule
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Energy (electron volt)
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1 hp
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= 746 joule/sec
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Power (horse power, ft-lb)
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1 psi
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= 6,890 newton/m2
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Pressure (pound per square inch)
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1 bar
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= 105
newton/m2
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Pressure
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1 atm
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= 1.013 x 105
newton/m2
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Pressure (atmospheric pressure)
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1 in-Hg
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= 3,386 newton/m2
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Pressure (inches mercury)
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Home
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Copyright ©
2004 Dr. Ranel E. Erickson
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