Powers of 10 and Scientific Notation

1. Powers of 10 and Scientific Notation Objective: Learn to use exponents to write powers of 10. Learn to write large numbers in scientific notation.

2. 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

3. 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 × 104 Example: Write each number in scientific notation. 31,700,000,000 2) 9,600.5

4. Examples: Write in scientific notation. * 93,000 * 1,030,000,000 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. Write in standard form. 1) 4.1 × 105 2) 2.894 × 1012 5.98 × 106 4) 1.32 × 1010

5. Homework: Write each number in standard form. • 8× 106 • 6 × 108 • 5.2 × 108 • 1.2 × 1012 • 4.98 × 105 • 2.368 × 1010 Write each number in scientific notation. • 9,370,000,000 • 8,500 • 175 • 10,100,000,000 • 243,000,000 • 439,300,000