Transcript 1.32 Scientific Notation

Introduction to
Chemistry
for Allied Health Sciences
Scientific Notation
Kirk Hunter
Chemical Technology Department
Texas State Technical College Waco
Scientific
Notation
SCIENTIFIC NOTATION
Any number can be written
as power of ten.
356 = 3.56 x 102
0.046 = 4.6 x 10-2
SCIENTIFIC NOTATION
• When you write numbers in
scientific notation, the decimal
is always after the first nonzero digit. This number is
called the coefficient.
• The power of ten is called the
exponent.
SCIENTIFIC NOTATION
• If the original number is greater
than ten, the exponent is positive.
Example: 325 = 3.25 x 102
• If the original number is less than
one, the exponent is negative.
Example: 0.00278 =2.78-3
SCIENTIFIC NOTATION
• Write the following numbers in
scientific notation.
125
0.546
40,897
23.4
1065
67
0.0732
0.0048
0.00035
SCIENTIFIC NOTATION
• Write the following numbers in
scientific notation.
125
0.546
1.25 * 102
5.46 *
2.34 * 101
1.065 * 103
23.4
0.0732
7.32 * 10-2
10-1
1065
40,897
4.0897 * 104
67
6.7 * 101
0.0048
0.00035
4.8 * 10-3
3.5 * 10-4
SCIENTIFIC NOTATION
Math operations
• Multiplication
(3.5 x 102) x (2.0 x 103) = ?
• Multiply the coefficients, add
exponents.
(3.5 x 2.0) x 10(2 + 3) = 7.0 x 105
SCIENTIFIC NOTATION
Math operations
Multiply the following:
A. (2.1 x 103)x (2.0 x 102)
B. (3.1 x 10-1) x (3.0 x 10-2)
C. (4.0 x 105) x (2.0 x 10-3)
SCIENTIFIC NOTATION
Math operations
• Division
4.2 x 104 / 2.0 x 102 = ?
• Divide the coefficients,
subtract the exponents
(4.2/2.1) x 10(4-2) = 2.1 x 102
SCIENTIFIC NOTATION
Math operations
Divide the following:
A. (3.4 x 105)/(1.7 x10-2)
B. (6.3 x10-3)/(2.1 x 10-3)
SCIENTIFIC NOTATION
Math operations
• Addition
(1 .5 X103)+ (2.3 X 102)+ (2.0 X 103)
All NUMBERS MUST HAVE THE SAME
POWERS OF TEN
(1.5 + 0.23 + 2.0) X 103 = 1.73 X 103
SCIENTIFIC NOTATION
Math operations
Add:
A. (2.0 X 104)- (3.0 X 103)
B. (6.4 X 102)+ (2.3 X 103) + (4.5 X 104)