SYSTEMS0.00000000000...2 etc.MATHEMATICS Decimal System 1 . = one 2 .. = two 3 ... = three 4 . . . . = four 5 . . . . . = five 6 . . . . . . = six 7 . . . . . . . = seven 8 . . . . . . . . = eight 9 . . . . . . . . . = nine 10 = 9 + 1 = ten 20 = 10 + 10 = twenty 30 = 20 + 10 = thirty 40 = 20 + 20 = forty 50 = 30 + 20 = fifty 60 = 40 + 20 = sixty 70 = 50 + 20 = seventy 80 = 40 + 40 = eighty 90 = 50 + 40 = ninety 100 = 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 0.11111111111...1 etc.0.99999999999...9These are small, infinitely repeating numbers.Rational numbers. These are numbers with values expressible in fractions and 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. Equations 1 + 1 = 2 2 + 3 = 5 2 * 10 = 20 1 / 10 = 0.1 1/100 = 0.01 1/1000 = 0.001 10 / 20 = 1/2 = 0.5 10X = Y = Y is exactly 10 * X That is the same as writing 10X - Y = 0. Squares and Square Roots 0 ^ 1 = 0 * 1 = 0 1 ^ 0 = 1 * 1 = 1 2 ^ 0 = 1 * 1 * 1 = 1 etc. 1 ^ 2 = 1 * 1 = 1 1 ^ 3 = 1 * 1 * 1 = 1 2 ^ 2 = 2 * 2 = 4 2 ^ 3 = 2 * 2 * 2 = 8 1 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 8 Multiplying with Exponents Add exponents that are multiplied: (2^2) (2^2) = 2 ^ 4 = 2 * 2 * 2 * 2 = 16 And 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) = - 4 2 ^ - 3 = - (2 ^ 3)= - 8 If an expression involving positive and negative numbers is multiplied, then BOTH RULES APPLY. For example, (2 ^ 3) (2 ^ -2) = 8 * - 4 = - 32 Fractions cancel with their integer and fractional opposites. For example, (2 ^ (1/2)) (2 ^ (-1/2)) = 1, because the 0.5s logically cancel out and 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) ^ 16 Now 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 Notation 1 X 10 ^1 = 10 1 X 10 ^2 = 100 1 X 10 ^ 3 = 1000 1 X 10 ^ 4 = 10,000 1 X 10 ^ 5 = 100,000 1 X 10 ^ 6 = 1,000,000 etc. Trans-Finite Numbers 1/ 0 = Infinity 2/ 0 = 2 * Infinity = Infinity Infinity * Infinity = Infinity Infinity / 2 = Infinity See also: Percentage to degreesKnowing geometryFactors of fractions (?)Grams to MolsFor more advanced material, see Calculus.BACK TO SYSTEMS |