Page 246 - Algebra 1

Scientific Notation
A number written as the product of two factors in the form a × 10n, where 1 ≤ a < 10 and n is an integer.
Example
1
Writing Numbers in Scientific Notation
Write each number in scientific notation.
a. 856,000
SOLUTION
Because this is a number greater than 1, the exponent will be positive.
The decimal point moves to be after the 8 so that there is one digit to the left of the decimal.
856,000. 54 321
Move the decimal five places, and write the number as 8.56000 × 105. So, 856,000 = 8.56 × 105.
b. 0.0005
SOLUTION
Because this is a number between 0 and 1, the exponent will be negative. The decimal point moves to be after the 5, so that there is one digit to its left.
0.0005. 123 4
Move the decimal four places, and write the number as 5 × 10-4.
To multiply numbers in scientific notation, multiply the coefficients and then multiply the powers. If the result is not in scientific notation, adjust it so that it is.
Multiplying Numbers in Scientific Notation
Find the product. Write the answer in scientific notation. (5.7 × 105)(1.8 × 103)
SOLUTION
(5.7 × 105)(1.8 × 103)
Caution
8.56 × 105 is in scientific notation.
85.6 × 104 is not in scientific notation.
Math Reasoning
Analyze Why is there no decimal point in the answer?
Example
2
= (5.7 · 1.8)(105 · 103) = 10.26 × 108
Use the Commutative and Associative Properties of Multiplication to group the numbers and the powers.
Simplify.
Hint
When you multiply powers with like bases, keep the base the same and add the exponents. 105 ·103 =105+3
Notice that the result is not in scientific notation. There is more than
one digit before the decimal point. Move the decimal to the left one place and add one to the exponent.
10.26 × 108 = 1.026 × 109
Lesson 37 231