SCIENTIFIC NOTATION FOR WRITING VERY BIG AND VERY

SCIENTIFIC NOTATION FOR WRITING VERY BIG AND VERY SMALL NUMBERS

• Easy to recognize because they are written as a power of ten • MX 8 10 MANTISSA: ONLY SIG FIGS. EXPONENT + = large # - = small #

TO WRITE A NUMBER IN SCIENTIFIC NOTATION • Find the sig. figs. • Move decimal between the 1 st and 2 nd sig. fig. → MANTISSA • # of spaces and direction moved → EXPONENT for the power of ten. left = positive right = negative

• PROPER scientific notation form can only have ONE DIGIT to the LEFT of the decimal

PRACTICE PROBLEMS • WRITE IN PROPER SCI. NOTATION FORM • 1) 405 000 000 mm • 2) 0. 000 000 670 cg

ANSWERS 11 10 mm • 1) 4. 05 X -10 • 2) 6. 70 X 10 cg

• MATH WITH SCI. NOTATION (and SIG FIGS) MULTIPLICATION – MULTIPLY MANTISSAS – ADD EXPONENTS. 3 2 • Ex. : (2. 5 X 10 )(6. 4 X 10 ) 3+2 5 WORK: (2. 5 * 6. 4) X 10 = 16 X 10 must correct for improper form • 6 FINAL ANSWER: 1. 6 X 10 ANSWER

Part of the work 2. 5 X 6. 4 100 150 16. 00

• DIVISION – DIVIDE MANTISSAS – SUBTRACT BOTTOM EXPONENT FROM TOP • Ex. : 4. 5 X 1012 / 3 X 10 -2 WORK: (4. 5 / 3) X 1012 –(-2) = 14 1. 5 x 10 14 • FINAL ANSWER: 2 x 10 ANSWER

Part of the work 1. 5 3 4. 5 3 15 15 0

• ADDITION – MUST HAVE SAME EXPONENT. ACHIEVED BY MOVING DECIMAL PT. IN THE MANTISSA – ADD MANTISSAS AND CARRY OVER EXPONENT.

3 2 • Ex. : (1. 5 X 10 ) + (3 X 10 ) = ? • WILL NOT MATTER WHICH EXPONENT YOU CHANGE; WILL CHANGE 2 TO A 3 • MOVE DECIMAL ONE PLACE TO LEFT (positive move) NOW NUMBER BECOMES. 3 X 103 WORK: (1. 5 X 103) + (. 3 X 103) = 1. 8 X 103 • FINAL ANSWER: 1. 8 X 103

Part of the work 1. 5 • 0. 3 3 • 1. 8 X 10 •

• SUBTRACTION – MUST HAVE SAME EXPONENT. ACHIEVED BY MOVING DECIMAL PT. IN THE MANTISSA – SUBTRACT MANTISSAS AND CARRY OVER EXPONENT.

-3 -2 • Ex. : (2. 1 X 10 ) – (5 X 10 ) = ? • WILL CHANGE – 3 TO A – 2 • MOVE DECIMAL TO LEFT ONE SPACE (positive move) NOW NUMBER BECOMES. 21 X 10 -2 WORK: (. 21 X 10 -2) – (5 X 10 -2) = -2 -4. 79 X 10 -2 • FINAL ANSWER: ANSWER -5 X 10

Part of the work • 0. 21 • 5 OR -5 0. 21 -2 -4. 79 X 10

PRACTICE PROBLEMS COPY AND WORK. ANSWERS MUST BE IN SCI. NOTATION WITH CORRECT SIG FIGS. 1) 2) 3) 4) (6. 78 x 1028) + (3. 345 x 1027) =? -12 -11 (4. 3 x 10 ) – (7. 89 x 10 ) =? (2. 75 x 1025)(3. 3 x 10 -34) =? 8 -12 (7. 20 x 10 ) / (1. 2 x 10 )=?

ANSWERS 1) 2) 3) 4) 28 10 7. 11 x -11 -7. 46 x 10 -9 9. 1 x 10 20 6. 0 x 10