1. 7-2 Scientific Notation
Hubarth
Algebra

2. Scientific Notation
A number in scientific notation is written as the product of two factors in the form
a x 10 𝑛 , where n is an integer and 1≤𝑎<10.
Example 3.4 x x x 10 −10
When converting to scientific notation
moving the decimal to the left gives you a positive exponent ,000 = 3.5 x 10 4
moving the decimal to the right gives you a negative exponent = 2.96 x 10 −3

3. Ex 1 Recognizing Scientific Notation
Is each number written in scientific notation? If not, explain.
a  104
No; 0.46 is less than 1.
b  10–2
yes
c  106
No; 13.2 is greater than 10.

4. Ex 2 Writing a Number in Scientific Notation
Write each number in scientific notation.
a. 234,000,000
Move the decimal point 8 places to the left and use 8 as an exponent.
234,000,000 =
Drop the zeros after the 4.
2.34  108 b
Move the decimal point 5 places to the right and use –5 as an exponent. =
6.3  10–5
Drop the zeros before the 6.

5. Ex 3 Writing a Number in Standard Notation
Write each number in standard notation.
a. elephant’s mass: 8.8  104 kg
8.8  104 =
A positive exponent indicates a number greater than 10. Move the decimal point 4 places to the right.
= 88,000 kg
b. ant’s mass: 7.3  10–5 kg  
7.3  10–5 =
A negative exponent indicates a number between 0 and 1. Move the decimal point 5 places to the left.
= kg

6. Ex 4 Application
List the planets in order of their distance from the
sun from least to greatest.
Jupiter
Earth
Neptune
Mercury
4.84  108 mi
9.3  107 mi
2.8  109 mi
3.8  107 mi
Planet
Distance from
the Sun
3.8     109
Mercury Earth Jupiter Neptune
From least to greatest distance from the sun, the order of the planets is Mercury, Earth, Jupiter, and Neptune.

7. Ex 5 Using Scientific Notation to Order Numbers
Order  105, 6.03  104, 6103, and 63.1  103 from least to greatest.
Write each number in scientific notation.
   103
6.3     104
Order the powers of 10. Arrange the decimals with the same power of 10 in order.
6.3     104
Write the original numbers in order.
   103

8. Ex 6 Multiplying a Number in Scientific Notation
Simplify. Write each answer using scientific notation.
Use the Associative Property of Multiplication.
(6 • 8)  10–4 = a.
6(8  10–4)
= 48  10–4
Simplify inside the parentheses.
= 4.8  10–3
Write the product in scientific notation.
Use the Associative Property of Multiplication.
(0.3 • 1.3)  103 = b.
0.3(1.3  103)
= 0.39  103
Simplify inside the parentheses.
= 3.9  102
Write the product in scientific notation.