Learning Target: I can use exponents to show powers of 10.

Powers of 10 with Exponents

The product that results from multiplying ten by itself is called a "power of 10."

We use powers of 10 to write very large or very small numbers.

Ten is the base, and the number of times 10 is multiplied by itself is the exponent.

Example 1

Example 2

Facts about Powers of 10:

• Positive exponents show numbers greater than 1
• Negative exponents show numbers less than 1
• For positive exponents, the exponent tells the number of zeros after 1
• For negative exponents, the exponent tells the number of places after the decimal point

You can write whole numbers and decimals in expanded form using powers of 10:

Example 3

Let's Practice Together

1.  Write 100,000 as a power of 10.

2.  Write 350.72 in expanded form using powers of 10.

Your Turn

Write each number as a power of 10:

3.)

10,000

4.)

1,000

5.)

0.0001

6.)

0.001

7.)

100,000,000,000

Write each number in expanded form using powers of 10:

8.)

3,000

9.)

2,350,000,000

10.)

7.321

Write each number in standard form:

11.)

12.)

Check for Understanding

1.)  Mt. Everest, the world's tallest mountain, is 29,028 feet high.  Express this number in expanded form using exponents.

Answers

1.  105

2.  (3 x 102) + (5 x 101) + (7 x 10-1) + (2 x 10-2)

3.  104

4.  10³

5.  10^-4

6.  10^-3

7.  10¹¹

8.  3 x 10³

9.  (2 x 10⁹) + (3 x 10⁸) + (5 x 10⁷)

10.  (7 x 10⁰) + (3 x 10^-1) + (2 x 10^-2) + (1 x 10^-3)

11.  23,050

12.  0.4958

Check for Understanding

1.  (2 x 104) + (9 x 103) + (2 x 101) + (8 x 100)