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Powers of 10 and Scientific Notation

Objective:

Learn to use exponents to write powers of 10.

Learn to write large numbers in scientific notation.

You have seen some numbers that are too large to be written down easily. Today you’ll

learn a method created by scientists that make it easier to write and work with very

large numbers.

A number like 1000 can be written a as 10 × 10 ×10. When factors are repeated, you can use an exponent and a base.

You can write 10 × 10 ×10 as 103 because there are the three 10s multiplied together.

The product 1000 is called a power of 10. 10, 100, 1000, 10000, are also powers of 10.

3 factors Example: Evaluate 104

10 × 10 ×10

Evaluate 109

103

Base

The numbers you have seen so far have been written in standard form. The number 88,000 is written in Standard Form. But it can also be expressed in powers of 10.

Scientific Notation is a way of writing large numbers.A number in scientific notation has 3 parts:

a number greater than × a power of 10 or equal to 1 but less than 10

Example: 8.8 × 104Example: Write each number in scientific notation.1) 31,700,000,000

2) 9,600.5

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To write the numbers in standard form: To write the numbers in standard form, you must move the decimal point the same amount of spaces as the exponent.

Examples: Write in scientific notation. * 93,000

* 1,030,000,000

Write in standard form. 1) 4.1 × 105

2) 2.894 × 1012

3) 5.98 × 106

4) 1.32 × 1010

Homework:

Write each number in standard form.

1.8× 106

2.6 × 108

3.5.2 × 108

4.1.2 × 1012

5.4.98 × 105

6.2.368 × 1010

Write each number in scientific notation.

7. 9,370,000,000

8. 8,500

9. 175

10. 10,100,000,000

11. 243,000,000

12. 439,300,000