SCIENTIFIC NOTATION

FOR WRITING VERY BIG AND VERY SMALL NUMBERS

• Easy to recognize because they are written as a power of ten

• M X 108

MANTISSA: ONLY SIG FIGS.

EXPONENT+ = large #- = small #

TO WRITE A NUMBER IN SCIENTIFIC NOTATION

• Find the sig. figs.

• Move decimal between the 1st and 2nd sig. fig. → MANTISSA

• # of spaces and direction moved → EXPONENT for the power of ten.

left = positive right = negative

• PROPERPROPER scientific notation form can only have ONE DIGITONE DIGIT to the LEFTLEFT of the decimal

PRACTICE PROBLEMS• WRITE IN PROPER SCI. NOTATION

FORM

• 1) 405 000 000 000 mm

• 2) 0.000 000 000 670 cg

ANSWERS

• 1) 4.05 X 1011mm

• 2) 6.70 X 10-10cg

MATH WITH SCI. NOTATION (and SIG FIGS)• MULTIPLICATION

– MULTIPLY MANTISSAS– ADD EXPONENTS.

• Ex.: (2.5 X 103 )(6.4 X 102)

WORK: (2.5 * 6.4) X 103+2 = 16 X 105 must correct for improper form

• FINAL ANSWERFINAL ANSWER: 1.6 X 106

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) =

1.5 x 1014

• FINAL ANSWERFINAL ANSWER: 2 x 1014

Part of the work

3

3

1 5

1 5

0

4.5 1.5

• ADDITION

– MUST HAVE SAME EXPONENT. ACHIEVED BY MOVING DECIMAL PT. IN THE MANTISSA

– ADD MANTISSAS AND CARRY OVER EXPONENT.

• Ex.: (1.5 X 103) + (3 X 102) = ?• 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

• 1.8 X 103

• SUBTRACTION

– MUST HAVE SAME EXPONENT. ACHIEVED BY MOVING DECIMAL PT. IN THE MANTISSA

– SUBTRACT MANTISSAS AND CARRY OVER EXPONENT.

• Ex.: (2.1 X 10-3) – (5 X 10-2) = ?• 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) =

-4.79 X 10-2

• FINAL ANSWERFINAL ANSWER: -5 X 10-2

Part of the work

• 0.21 -5

• 5 OR 0.21

-4.79 X 10-2

PRACTICE PROBLEMSCOPY AND WORK. ANSWERS MUSTBE IN SCI. NOTATION WITH CORRECTSIG FIGS.

1) (6.78 x 1028) + (3.345 x 1027) =?

2) (4.3 x 10-12) – (7.89 x 10-11) =?

3) (2.75 x 1025)(3.3 x 10-34) =?

4) (7.20 x 108) / (1.2 x 10-12)=?

ANSWERS

1) 7.11 x 1028

2) -7.46 x 10-11

3) 9.1 x 10-9

4) 6.0 x 1020