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 turn the multiplied expression into 1 divided by the original expression raised to the absolute number or positive value of the negative exponent. For example, 2 ^ - 2 = 1 / 2 ^ 2 = 1/4 2 ^ - 3 = 1 / 2 ^ 3 = 1/8 Note that these are just fractional powers of 2. If an expression involving positive and negative numbers is multiplied, then BOTH RULES APPLY. (2 ^ 2) (2 ^ -2) = 1 / (2 * 2 ^ 2) = 1 / 16 And indeed, 4 * 1/16 is a 1/4 of a 1/4 which is 1/16. In the case of multiplying negative exponents, the result is also multiplication. In the case of pre-existing exponents in fractions, the advice is to simplify them by computing values or multiplying or dividing multiple groups by the opposite of the extracted fraction. 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 that might be considered irreducible without doing a further calculation. 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 For more advanced material, see Calculus.BACK TO SYSTEMS |