SCIENTIFIC NOTATION Lesson 8-2 A QUICK WAY TO WRITE REALLY, REALLY BIG OR REALLY, REALLY SMALL NUMBERS.

We can write multiples of 10’s using exponents 10000 = 10 x 10 x 10 x 10 = 104 1000 = 10 x 10 x 10 = 103 100 = 10 x 10 = 102 10 = 101 1 = 100 Do you see a pattern?

Sooooo negative exponents come from multiplying tenths = 10-1 = = 10-2 = = 10-3 = = 10-4

Rules for Scientific Notation To be in proper scientific notation the number must be written with * a number between 1 and 10 * and multiplied by a power of ten 23 X 105 is not in proper scientific notation. Why?

A number written in Scientific Notation has three parts… A number greater than one but less than ten A power of ten A multiplication sign

1. Move the decimal to the right of the first non-zero number. To write a number in scientific notation: 1. Move the decimal to the right of the first non-zero number. 2. Count how many places the decimal had to be moved. 3. If the decimal had to be moved to the right, the exponent is negative. 4. If the decimal had to be moved to the left, the exponent is positive.

Soooo 137,000,000 can be rewritten as 1.37 X 108

Using scientific notation, rewrite the following numbers. Now You Try Using scientific notation, rewrite the following numbers. 347,000. 902,000,000. 61,400.

Using scientific notation, rewrite the following numbers. Now You Try Using scientific notation, rewrite the following numbers. 347,000. 3.47 X 105 902,000,000. 9.02 X 108 61,400. 6.14 X 104

Convert these to standard notation: 1.23 X 105 6.806 X 106

Convert these to standard notation: 1.23 X 105 123,000 6.806 X 106 6,806,000

In the United States, 15,000,000 households use private wells for their water supply. Write this number in scientific notation. 1.5 X 107

Using Scientific Notation, rewrite the following numbers. Your Turn Using Scientific Notation, rewrite the following numbers. 0.000882 0.00000059 0.00004

Using Scientific Notation, rewrite the following numbers. Your Turn Using Scientific Notation, rewrite the following numbers. 0.000882 8.82 X 10-4 0.00000059 5.9 X 10-7 0.00004 4 X 10-5

.000007 The nucleus of a human cell is about 7 X 10-6 meters in diameter. What is the length in standard notation? .000007

Proper Scientific Notation Which way did the decimal move? You can think of this as going the opposite direction If you move the decimal to the left: The exponent goes UP 88.2 X 103 = 8.82 X 10 ? 8.82 X 10 4 If you move the decimal to the right: The exponent goes DOWN 0.45 X 103 = 4.5 X 10 ? 4.5 X 10 2 154.7 X 10 -6 =

Proper Scientific Notation Negative exponents follow the same rules You can think of this as going the opposite direction If you move the decimal to the left: The exponent goes UP If you move the decimal to the right: The exponent goes DOWN 154.7 X 10 -6 = 0.048 X 10 -3 =

You Try 55.6 x 10 4 .067 x 10 12 - 415.1 x 10 -8 23.1 x 10 -4 102 x 10 5 -2.3 x 10 3

Multiplication with Scientific Notation Lesson 8-3 Review

Multiplication with Scientific Notation Multiply the decimal numbers together. Add the exponents to get the power of 10. Sample Problem: Multiply (3 x 10-3) (2 x 105) Solution: Multiply 3 x 2. Add the exponents -3 + 5 Answer: 6 x 102

Example Given: 2 (4 X 106) Multiply decimals: 2 X 4 = 8 Add Exponents: 100 x 106=100+6=106 Answer: 8 X 106

Example Given: 3.4 X 105 • 4.0 X 109 Multiply decimals: 3.4 X 4.0 = 13.6 Add Exponents: 105 x 109=105+9=1014 Preliminary Answer: 13.6 X 1014 Now, Rewrite in Scientific Notation if needed. Final Answer: 1.36 X 1015

Given: (2 X 10-2) • (6 X 10-5) Your Turn Multiply Decimals: 2 X 6 = 12 Add Exponents: 10-2 x 10-5=10-2+(-5)=10-7 Answer: 12 X 10-7 Rewrite in Scientific Notation Final Answer: 1.2 X 10-6

Warm Up

Dividing Numbers in Scientific Notation Lesson 8-5 continued

Dividing Numbers in Scientific Notation Divide the decimal numbers. Then subtract the exponents

Example 1 Given: 8 • 10-7 2 • 10-2 Divide decimals: 8÷2 = 4 Subtract exponents: (-7)-(-2)= -5 Final Answer: 4 •10-5

Example 2 Given: 1.6 X 103 8 X 104 Divide decimals: 1.6 ÷ 8= 0.2 Subtract exponents: 3 - 4 =-1 Preliminary Answer: 0.2 X 10-1 Now, Rewrite in Scientific Notation if needed. Final Answer: 2.0 X 10-2

Your Turn Given: 3.4 X 102 2 X 10-5

Your Turn Given: 3.4 X 102 2 X 10-5 Divide decimals: 3.4 ÷ 2= 1.7 Subtract exponents: 2- (-5) =7 Answer: 1.7 X 107

Try a few more

Using a Calculator The “E” or “e” or “exp” means the exponent in scientific notation