• 1 meter (m) = 39.4 inches = 1.09 yards; 1 yard = 0.92 m
• 1 centimeter (cm) = 0.39 inches; 1 inch = 2.54 cm
• 1 millimeter (mm) = 0.039 inch = 39/1,000 inch; 1 inch = 25.4 mm
• 1 micrometer or micron (um) = 0.000039 inch = 39/1,000,000 inch;
• 1/1000 inch = 25.4 um
  
• 1gram (g) = 0.035 oz = 35/1,000 oz; 1 oz = 28.3 g
• 1 kilogram (1,000g, 1Kg) = 2.20 lb; 1 lb = 0.454 Kg
• 1 milligram (mg) = 0.000,035 oz; 1/1000 oz = 28.3 mg (a very small pinch of salt is about 1 mg)

Other Physical units

• decibel (dB) is the unit of sound power. It is a logarithmic scale, so 40dB = 10x20dB and 60dB = 10x40dB.
• volt (V) is the unit of electrical potential or "pressure". High voltage means that lots of "pressure" is pushing electrical energy. A common "battery" (technically, dry cell) like the D cell for most flashlights puts out 1.5V. The electric outlets in your house deliver 110V.
• Ampere (A, amp) is the unit of electrical current or "volume". High current means a lot of electricity is available. Older houses were built with 15 A circuits (and fuses or circuit breakers set to shut off above 15A. Newer houses have 20 and 30 A circuits.

Prefixes: multipliers

(X = multiply by, times)

• nano (n) = X 1/1,000,000,000 or 0.000,000,001
• micro (µ) = X 1/1,000,000 or 0.000,001
• milli (m) = X 1/1,000 or 0.001
• centi (c) = X 1/100 or 0.01
• deci (d) = X 1/10 or 0.1
• Kilo (k) = X 1,000
• Mega (M) = X 1,000,000

For example,

• a nanometer is 1/1,000,000,000 meter (see conversion to English units below)
• a millisecond (msec.) is 1/1,000 second.
• a microamplere (µA) is 1/1,000,000 amperes (unit of electric current). By comparison, an ordinary 60-watt lamp draws 0.6 Amperes.
• a kilocycle (kiloHertz or kHz) is 1,000 cycles/second
• a centimeter (cm) is 1/100 of a meter (or ~.4 inches)
• a decibel (dB) is 1/10 of a bel (unit of sound power)

Fraction, Proportion, Per Cent

A fraction is the number of times X₁ occurs compared to X_all. Suppose Sammy Rodriguez had 387 at bats and 121 hits last season. the fraction of hits compared to total at bats is 121/387.

A proportion is a fraction in which the numerator (top number) is divided by the denominator (bottom number). This is the same as

1. multiplying the denominator by the number that makes it 10 (or 10 multiplied by itself any number of times: 100, 1000, etc.)
2. multiplying the numerator by the same number
3. removing the 10 (or 100 or 1000, etc) denominator and moving the decimal point 1 (or 2 or 3, etc.) place(s) to the left.

A per cent is a proportion multiplied by 100, so Sammy makes a hit on 31.3% of his at bats.