SCIENTIFIC NOTATION Abbreviating numbers What is an EXPONENT
SCIENTIFIC NOTATION: Abbreviating numbers
What is an EXPONENT? i A SUPERSCRIPT after “x 10” or “E” i Ex: “x 105” or “E 5” i Denotes how many powers of ten i 105 = 10 x 10 i Answer is a 1 followed by zeros (defined by the exponent) 100, 000
BIG NUMBERS Positive Exponents 5, 987, 774, 231, 541
Numbers smaller than 1 Negative Exponents 0. 0000076319
Moving the decimal (+) MOVE THE DECIMAL TO THE RIGHT
Moving the Decimal (-) MOVE THE DECIMAL TO THE LEFT
PRACTICE: 1. 2. 3. 4. 67 x 105 1. 94 x 101 7. 69 x 100 2. 48 x 10 -2 = 467000 = 19. 4 = 7. 69 = 0. 0248 = 0. 00000735 = 0. 000252
Converting to Scientific Notation 1. FIND THE DECIMAL 2. MOVE THE DECIMAL SO THE BASE NUMBER IS LESS THAN 10, GREATER THAN 1 3. COUNT THE NUMBER OF JUMPS
Cont. 4. ROUND ANSWERS SO THEY HAVE THREE (3) DIGITS STARTING FROM THE LEFT 5. ADD “X 10” (or E) 6. THE NUMBER OF JUMPS IS YOUR EXPONENT!
PRACTICE: 56420 2. 123 3. 718134 4. 6132 1. 4 10 = 5. 64 x 2 = 1. 23 x 10 5 = 7. 18 x 10 3 = 6. 13 x 10
NEGATIVE EXPONENTS If your number is less than 1 you will have a negative exponent!
PRACTICE: 1. 2. 3. 4. 0. 0184 0. 000567 0. 06 0. 00057912347 = 1. 84 x 10 -2 = 5. 67 x 10 -4 -2 = 6. 00 x 10 -4 = 5. 79 x 10
Three Number Rule o If there are not enough numbers add zeros o If there are too many numbers round
Rounding 1. START FROM THE LEFT AND COUNT THE FIRST 3 NUMBERS 2. IF THE FOURTH NUMBER IS A 5 OR ABOVE ROUND UP! 3. DROP UNNECESSARY NUMBERS
PRACTICE: Put the problem in Sci. Not. 1 st : Round 1. 2. 3. 4. 5. 6. 23794 0. 0001146 468992 0. 9999 2100100 0. 000002 =2. 38 x 104 =1. 15 x 10 -4 =4. 69 x 105 =1. 00 x 100 =2. 10 x 106 =2. 00 x 10 -6
SCIENTIFIC NOTATION PRACTICE Convert the following to normal notation: 1. 5. 23 x 103 2. 2. 90 x 10 -9 3. 4. 18 x 10 -5 4. 2. 71 E 7 1. 2. 3. 4. Convert the following to SCIENTIFIC notation (ROUND T DIGITS): 0. 00854 349001 0. 03 1238 Round to 3 DIGITS (you have to put them in sci. not. first n n n 6349 0. 3487 7956143278
Prefixes: n Super¡ ¡ Above Ex: X 2 n Sub¡ ¡ Below Ex: X 2
Exponent Rule! DECIMAL MOVES n EXPONENT becomes MORE POSITIVE (+1) n DECIMAL MOVES n EXPONENT becomes MORE NEGATIVE (-1) n -2 -3 -2 0. 214 2. 14 xx 10 10
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