Scientific Notation

Rule

A number is written in scientific notation if it has the following form:

 c x 10ⁿ where 1 < c < 10 and n  is an integer.

Examples

Writing Numbers in Scientific Notation

Example 1

The thickness of a soap bubble is about 0.000004 meter. 

Write the number in scientific notation.

Example 2

There are over 300,000,000,000 stars in the Andromeda Galaxy. 

Write the number in scientific notation.

Writing Numbers in Standard Form

Example 1

Example 2

Multiplying Numbers in Scientific Notation

You can use the Product of Powers Property to multiply two numbers written in scientific notation.

Example

Find the product (4.5 x 10 ³) x (6.3 x 10 ⁷).

Guided Practice  (Ask your tutor for help.)

1)  Tell whether the number is expressed in scientific notation.

7 x 10 ^{- 4}                                                        

yes

^no

                     

 

 

2)  The mass of Earth is about 1.3 X 10²⁵ pounds. The mass of Jupiter is about 4.2 X 10²⁷ pounds.  About how many times greater is Jupiter's mass than Earth's mass?  

Hint

Step 1   Write the quotient of 4.2 and 1.3 as a decimal.
Step 2   Write the quotient of the powers of 10.
Step 3   Write the product of the quotients in scientific notation.

3)  In 2000, there were approximately 281,000,000 people in the United States.  Which of the following is not another way of expressing the number 281,000,000?

A.  28.1 million

B.  0.281 billion

C.  28.1 x 10 ⁷

D.  2.81 x 10 ⁸  

4)  In the United States, 15,000,000 households use private wells for their water supply.  Write this number in scientific notation.

5)  The United States has a total of 1.2916 x 10⁷ acres of land reserved for state parks.  Write this number in standard form.

6)  Write the number in scientific notation.

    0.0000000342

7)  Write the numbers in standard form.

6.35 x 10 ^{- 6}

 

 

 

2.83 x 10 ¹²