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