SYSTEMSMATHEMATICSDecimal System1 . = one2 .. = two3 ... = three4 . . . . = four5 . . . . . = five6 . . . . . . = six7 . . . . . . . = seven8 . . . . . . . . = eight9 . . . . . . . . . = nine10 = 9 + 1 = ten20 = 10 + 10 = twenty30 = 20 + 10 = thirty40 = 20 + 20 = forty50 = 30 + 20 = fifty60 = 40 + 20 = sixty70 = 50 + 20 = seventy80 = 40 + 40 = eighty90 = 50 + 40 = ninety100 = one hundred (90 + 10)200 = two hundred (100 + 100)1000 = one thousand (500 + 500)1,000,000 = one million (1000 * 1000)Infinitesimal numbers = 0.00000000000...1                    0.00000000000...2 etc.                    0.11111111111...1 etc.                    0.99999999999...9These are small, infinitely repeating numbers.Rational numbers.These are numbers with values expressible in fractionsand mathematical relationships.X = any number.Y = any number, possibly different from X.Z= any number, possibly different from X and Y 10X = 10 of any number. X / Y = Any number divided by any number. 3X / Y = Any number divided by any number in which 3X tends to be three times larger than Y.Equations1 + 1 = 22 + 3 = 52 * 10 = 201 / 10 = 0.11/100 = 0.011/1000 = 0.00110 / 20 = 1/2 = 0.510X = Y = Y is exactly 10 * XThat is the same as writing 10X - Y = 0.Squares and Square Roots0 ^ 1 = 0 * 1 = 01 ^ 0 = 1 * 1 = 12 ^ 0 =  1 * 1 * 1 = 1 etc.1 ^ 2 = 1 * 1 = 11 ^ 3 = 1 * 1 * 1 = 12 ^ 2 = 2 * 2 = 42 ^ 3 = 2 * 2 * 2 = 81 root of any number is that number.The 2 root of any number is the square root of that number.The square root of 4 is 2, because two 2s multiply to equal 4.Number    Sq. Rt.-----------------------------    4               2    9               3   16              4   25              5   36              6   49              7   64              8Multiplying with ExponentsAdd exponents that are multiplied:(2^2) (2^2) = 2 ^ 4 = 2 * 2 * 2 * 2 = 16And we know that 2 ^ 2 is 2*2 which is 4, and 4 * 4 is 16.If a negative exponent is alone, simply take the value using a regular exponent, and then add a minus sign.For example,2 ^ - 2 = - (2 ^ 2) =  - 42 ^ - 3 =  - (2 ^ 3)=  - 8If an expression involving positive and negative numbers is multiplied, then BOTH RULES APPLY.For example,(2 ^ 3) (2 ^ -2) = 8 * - 4 = - 32Fractions cancel with their integer and fractional opposites.For example,(2 ^ (1/2)) (2 ^ (-1/2)) = 1, because the 0.5s logically cancel outand we are left with 2 ^ 0 * 2 ^0, which is just 1*1.The multiplication of positive and negative exponents is an exception where you can work across the parentheses.In the case of multiplying negative exponents, the result is also multiplication of the specific exponents.In the case of pre-existing exponents in fractions, the advice is to simplify them by 1. computing values, and 2. if possible, extracting any identical exponents.For example,(4 / 2 ^ 16) + (2 / 3 ^ 16) could reduce to:(4/2 + 2/3) ^ 16Now we would either just enter it into our calculator, or multiply the 2 and 3 or 2/3rds by 2 to equal 4 / 6 and the 4 and the 2 of 4/2 by 3 to equal 12/6 and we get (12/6 + 4/6) ^ 16 = (16/6) ^ 16. At this point unless we can reduce the fraction it then might be considered irreducible without doing a further calculation.However, we can reduce the fraction to 8/3, so now we get(8/3) ^16, which is less interesting if it is fully calculated.Scientific Notation1 X 10 ^1 = 101 X 10 ^2 = 1001 X 10 ^ 3 = 10001 X 10 ^ 4 = 10,0001 X 10 ^ 5 = 100,0001 X 10 ^ 6 = 1,000,000 etc.Trans-Finite Numbers1/ 0 = Infinity2/ 0 = 2 * Infinity = InfinityInfinity * Infinity = InfinityInfinity / 2 = InfinitySee also:Percentage to degreesKnowing geometryFactors of fractions (?)Grams to MolsFor more advanced material, see Calculus.BACK TO SYSTEMS