MEASUREMENTS & CONVERSIONS
LengthVolumeMass
Basic Unitmeter (m)liter (l)gram (g)
X10decameter (dam)deciliter (dal)decagram (dag)
X100hectometer (hm)hectoliter (hl)hectogram (hg)
X1000kilometer (km)kiloliter (kl)kilogram (kg)
÷10decimeter (dm)deciliter (dl)decigram (dg)
÷100centimeter (cm)centiliter (cl)centigram (cg)
÷1000millimeter (mm)milliliter (ml)milligram (mg)
- Metric ton is defined as 1000kg
English System
LengthVolume
1 foot (ft or ‘) = 12 inches (in or “)1 tablespoon (tbl) = 3 teaspoons (tsp)
1 yard (yd) = 3 feet1 cup (c) = 16 tablespoons
1 mile (mi) = 1760 yards = 5280 feet1 pint (pt) = 2 cups
1 nautical mile = 1.15 miles1 quart (qt) = 2 pints
1 league = 3 miles1 gallon (gal) = 4 quarts
WeightArea
1 pound (lb) = 16 ounces (oz)1 acre = 4840 sq. yards = 43,560 sq. feet
1 ton = 2000 pounds1 sq. mile = 640 acres
CONVERSION TABLE
When You KnowMultiply ByTo Find
Inches2.54centimeters
Feet30.48centimeters
Yards0.9144meters
Miles1.609kilometers
Teaspoons4.9289milliliters
Tablespoons14.787milliliters
Cups0.2366liters
Pints0.4732liters
Quarts0.9464liters
Gallons3.7854liters
Pounds0.4536kilograms
Tons0.9072metric tons
Centimeters0.3937inches
Meters1.0936yards
Kilometers0.6214miles
Milliliters0.0338fluid ounces
Liters1.057quarts
Liters0.2642gallons
Grams0.0353ounces
Kilograms2.2046pounds
Metric tons1.1023tons
SCIENTIFIC NOTATION
All numbers are to be expressed as Mx 10n M must fit 1≤ M ≤ 10
N is an integer, positive or negative
Converting TO Scientific Notation
If decimal point has to be moved left – powers are increasing
If decimal point has to be moved right – powers are decreasing
Converting FROM Scientific Notation
If power is positive – move decimal right
If power is negative – move decimal left
Math Operations Using Scientific Notation
Addition or Subtraction
1.Make sure that the powers of ten are the same. Convert to larger if necessary.
2.Do the addition or subtraction.
3.Evaluate your answer. A) Check to make sure that it is in proper scientific notation.
B) Make sure that it has the proper number of significant digits.
Multiplication
1.Multiply the numbers together.
2.Add the powers together.
3.Evaluate your answer. A) Check to make sure that it is in proper scientific notation.
B) Make sure that it has the proper number of significant digits.
Division
1.Divide the numbers
2.Subtract the powers.
3.Evaluate your answer. A) Check to make sure it is in proper scientific notation.
B) Make sure that it has the proper number of significant digits.
SOLVING EQUATIONS – MANIPULATING EQUATIONS
When you are manipulating an equation to solve for a specific variable; the variable you want should end up on the left side of the equation, by itself.
1.Rearrange the formula so that the variable you are solving for is on the left side of the “=” sign.
2.If the variable you are solving for is under a square root sign, square everything on each side of the equation.
3.If the variable you are solving for is on the bottom of a fraction, multiply each side by that variable. Rearrange to get the variable you are solving for on the left side.
4.If the variable you are solving for is being divided by anything, multiply each side by what the variable is being divided by. (You may do more than one at a time.)
5.If the variable you are solving for is being multiplied to anything, divide each side by what the variable is being multiplied to. (You may do more than one at a time.)
6.If the variable you are solving for is being squared, take the square root of each side of the equation.
7.Cancel out any variables or numbers where you can.
RIGHT TRIANGLE TRIGONOMETRY
Cosine θ = adjacent / hypotenuseSine θ = opposite / hypotenuse Tangent θ = opposite / adjacent
Hypotenuse 2 = adjacent2 + opposite 2 c2 = a2 + b2orc = √a2 + b2