Page 247 - Algebra 1

To divide numbers in scientific notation, divide the coefficients, and then divide the powers. If the result is not in scientific notation, adjust it so that it is.
Dividing Numbers in Scientific Notation
F_ i n d t h e q u o t i e n t . W r i t e t h e a n s w e r i n s c i e n t i f i c n o t a t i o n . 1.2 × 103
9.6 × 106 S_OLUTION
1.2 × 103 9.6 × 106
= 1.2 × 10 _ _3
9.6 106
= 0.125 × 10-3
Example
3
Hint
When you divide powers with like bases, keep
the base the same and subtract the exponents.
10 3-6 _3 =10 106
Divide the coefficients and divide the powers. Simplify.
Notice that this number is not in scientific notation. There is not one nonzero digit before the decimal point. Move the decimal to the right one place and subtract one from the exponent.
0.125 × 10-3 = 1.25 × 10-4
Comparing Expressions with Scientific Notation
Example
4
Compare. Use <, >, or =. 7.2 × 10 1.05 × 10
_6 _7 3.6 × 104 3.5 × 105
SOLUTION
7.2 × 10 1.05 × 10 _6 _7
3.6 × 104
= 7.2 ×10
3.5 × 105 =1.05×10
_ _6 3.6 104
_ _7 3.5 105
=0.3×102 =30 _6 _7
3.6 × 104 3.5 × 105 Application: SpeedofLight
The speed of light is 3 × 108 meters per second. If Earth is 1.47 × 1011 meters from the sun, how many seconds does it take light to reach Earth from the sun? Write the answer in scientific notation.
S_OLUTION Divide the earth’s distance from the sun by the speed of light.
1.47 × 1011
3 × 108 = 0.49 × 10
= 4.9 × 102 Write the answer in scientific notation.
It takes light about 4.9 × 102 seconds to reach the earth from the sun.
=2×102 =200
Since200>30,then 7.2×10 > 1.05×10 .
Example
5
232 Saxon Algebra 1
3