Download Scientific Notation - Section 8-4

Scientific Notation - Section 8-4
Multiplying by Powers of 10
 If the exponent is positive, move the decimal point to the right
 If the exponent is negative, move the decimal point to the left
Example 1:
5x10 2 
8.23 x10 4 
1.23 x10 3 
4x10 1 
500
82,300
.00123
.4
Scientific Notation
When you use very large numbers like 5,800,000 or very small numbers like 0.000076, it is difficult to keep
track of the place value.
Number such as these can be written in Scientific Notation
Follow these steps to write a number from standard form to scientific notation.
For numbers with an absolute value greater than 1: For numbers with an absolute value between 0 & 1:
1.) Move the decimal to the LEFT until you
have a number a, 1  a  10
2.) Write the number you have left as your a
value.
3.) The number of places you moved the
decimal is your power of 10(n). Since you
moved the decimal to the LEFT make your
power of ten(n) positive.
5,800,00  5.8 x10 6
1.) Move the decimal point to the RIGHT until
you have a number a, 1  a  10 .
2.) Write the number you have left as your a
value.
3.) The number of places you moved the
decimal is your power of 10 (n). Since you
moved the decimal to the RIGHT make
your power of ten (n) negative.
0.000076  7.6 x10 5
Example 2:
Express each number in scientific notation.
a. 5,800,000
5.8 x 106
b. 0.000076 = 7.6 x 10-5
Your Turn!
Express each number in scientific notation.
a. 3,900,000,000 = 3.9 x 109
b. 0.0000035 = 3.5 x 10-6
Example 3:
Evaluate the expression. 400 x 2,000,000,000
(4.0 x 102) x (2.0 x 109)
(4.0 x 2.0)x(102x109)
8.0 x 1011
Example 4:
4.8 x103
Evaluate the expression.
1.6 x101
3
 4.8  10 
2


 1   3x10
 1.6  10 
Your Turn!
a. 2000 x 3,000,000,000
b.
7.5 x107
1.5 x104
2.0 x10 3 x3.0 x10 9 
2.0 x3.010 3 x10 9  
7
 7.5  10


 4
 1.5  10
6.0 x1012
3.0 x10 3

 

Follow these steps to write a number from scientific notation to standard form.
For numbers with positive powers of ten:
For numbers with negative powers of ten:
6.8 x 104 = 68,000
9.23 x 10-2 = .0923
Move the decimal n(the power of ten) places to the
right
Move the decimal n(the power of ten) places to the
left.
Metric Prefixes:
Prefix
Power of 10
Meaning
tera
1012
1,000,000,000,000
giga
109
1,000,000,000
mega
106
1,000,000
kilo
103
1,000
pico
10-12
.000000000001
nano
10-9
.000000001
micro
10-6
.000001
milli
10-3
.001