Download SCIENTIFIC NOTATION - Zachary High School

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 1st and
2nd 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) 405 000 000 000 mm
• 2) 0.000 000 000 670 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
•
FINAL 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) =
14
1.5 x 10
•
FINAL ANSWER: 2 x 1014
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
3
•
FINAL ANSWER: 1.8 X 10
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
-2
NUMBER BECOMES .21 X 10
WORK:(.21 X 10-2) – (5 X 10-2) =
-4.79 X 10-2
-2
•
FINAL 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