Transcript Convert from standard notation to scientific notation:

Rounding
 We need to round numbers because a
calculator often gives an answer with
more digits than are justified by the
precision of the measurements.
 Look at the digit to the right of the
one to be rounded. If it is
 Less than 5, # stays the same
 Greater than or equal to 5, # increases
by 1
But how do you determine how
many sig digs to round to?
 Multiplication and division
 The answer can have no more sig digs
than the measurement with the least
number of sig digs.
 EXAMPLE:
 2.4 x 15.82 = 38
 16.25 / 5.1442 = 3.159
But how do you determine how
many sig digs to round to?
 Addition and subtraction
 The answer has the same number of
digits to the right of the decimal point as
the measurement having the fewest
digits to the right of the decimal point.
 EXAMPLE:
 25.1 + 2.03 = 27.1
 5.44-2.6103 = 2.83
How do you do calculations with
scientific notation?
 Multiplication
 Multiply coefficients
 Add exponents
 Round
EXAMPLES:
 (2 x 106) x
 (3 x 106) x
(3 x 103)= 6 x 109
(3 x 10-3)= 9 x 103
How do you do calculations with
scientific notation?
 Division
 Divide coefficients
 Subtract exponents
 (numerator-denominator)
 Round
EXAMPLES:




(6
(4
(8
(6
x
x
x
x
106)
106)
10-6)
106)
/
/
/
/
(3 x 103)= 2 x 103
(2 x 10-3)= 2 x 109
(2 x 103)= 4 x 10-9
(3 x 109)= 2 x 10-3
How do you do calculations with
scientific notation?
 Addition and subtraction
 Adjust so exponents are equal
 Add or subtract coefficients
 Put answer in scientific notation
 Round
EXAMPLE:
(4.2 x 104) + (7.9 x 103)
You can do it different ways…
EXAMPLE:
 (4.2 x 104) + (7.9 x 103)
4.2 x 104
+ 0.79 x 104
4.99 x 104 = 5.0 x 104
42 x 103
+ 7.9 x 103
49.9 x 103 =
50. x 103 = 5.0 x 104
Convert from standard notation to
scientific notation:
a.
b.
c.
d.
e.
f.
g.
h.
0.0052
6 132
0.023
0.000 000 120
560 000
33 400
0.000 4120
38 000 000 000
Convert from scientific notation to
standard notation
a.
b.
c.
d.
e.
f.
g.
h.
7.050 X 103
4.000 05 X 107
2.350 X 104
1.5 X 10-3
2.105 X 10-2
7 X 1016
4.8 X 10-4
6.011 X 10-10
How many significant figures
a.
b.
c.
d.
e.
f.
g.
h.
804.05
0.014 403 0
1002
10020
10020.
400
30 000.
30 000.0
How many significant figures
a.
b.
c.
d.
e.
f.
g.
h.
0.000 625 000
6.02 x 1023
6.00 x 103
0.00001
0.00123
1.23 x 103
7430
0.006 700 0
Round to 3 significant figures
a.
b.
c.
d.
e.
f.
g.
h.
0.000 625 500
2.7851
6.036 x 103
0.00001232
0.0012499
1.23 x 103
7435
0.006 752
Multiply or divide (how many
sigfigs)
a. 3.20 X 102 m x 1.50 x 103 m
b. 2.5 x 10-3 m x 1.5 x 104 m
c. 1.54 X 102 L
2 x 101 min
d. 2.0 x 10-2 min
Add or subtract/how many sigfigs
a. 2.48 X 102 kg + 9.17 X 103 kg =
b. 7.70 X 10-1 mL - 7.2 X 10-2 mL=