Scientific Notation When would someone think of using

Scientific Notation When would someone think of using scientific notation?

You guessed right! • Scientific Notation is used when the actual numbers are too LARGE or too small. • Mostly in science • Small numbers from items impossible to see with the human eye • Large numbers too big to fit on the page • Makes calculations easier.

How to write in Scientific Notation • Get your number to be between 1 and 9 by moving the decimal to the left or right. • 1, 624, 000, 000 changes to 1. 624000000

How Many Spaces? • Count the number of spaces from the beginning decimal point to the new point. • Ex. 1. 624, 000, 000 (15 spaces)

Moving the Decimal Point • Copy all the whole numbers with the new decimal point : 1. 624

Power of Ten • Multiply the remaining number by 10 raised to the number of places the decimal point moved. • 1. 624 x 1015

Positive Exponent • Use a positive exponent if the decimal point moved to the left. • 392, 000. • 3. 92 x 100, 000 • 3. 92 x 105 • A large number to a smaller number - positive exponent

Negative Exponent • Use a negative exponent if the decimal point moved to the right. • . 00000432 • 4. 32 x 10 -6 • A small number to a larger number is a negative exponent.

Your Turn • 1. ) 29, 900 5. ) 222. 6 • 2. ) 0. 000033 6. ) 2, 230, 000 • 3. ) 883 7. ) 0. 0000002 • 4. ) 0. 0199 8. ) 17, 250

Answers 1. ) 29, 900 5. ) 222. 6 2. 99 x 104 2. 226 x 102 2. ) 0. 000033 6. ) 8, 230, 000 3. 3 x 10 -9 8. 23 x 106 3. ) 983 7. ) 0. 0000002 9. 83 x 102 2 x 10 -7 4. ) 0. 0199 8. ) 17, 250 1. 99 x 10 -2 1. 725 x 104

If given the information in SCIENTIFIC NOTATION how do you write out the number? EX. 1. 25 x 104 = ? STEP 1 - Write the whole numbers with the decimal. 1. 25 STEP 2 - If there is a POSITIVE exponent, count the number of spaces to the RIGHT of the decimal point to match the exponent. 1. 2500 = 12500

6. 4 x 10 -3 • STEP 3 - If there is a NEGATIVE exponent, count the number of spaces going to the LEFT of the decimal point to match the exponent. 006. 4 =. 0064

TRY THESE! Rewrite these numbers so they are no longer in scientific notation. • 1. ) 2. 27 x 10 -2 5. ) 1. 33586(105) • 2. ) 3. 772 x 104 6. ) 1. 33586(10 -5) • 3. ) 5. 6 X 10 -1 7. ) 4. 22 x 102 • 4. ) 9. 7 x 107 8. ) 8. 96 x 103

ANSWERS • 1. ) 2. 27 x 10 -2 0. 0227 • 2. ) 3. 772 x 104 37, 720 • 3. ) 5. 6 X 10 -1 0. 56 • 4. ) 9. 7 x 107 97, 000 5. ) 1. 33586(105) 133, 586. 6. ) 1. 33586(10 -5) 0. 0000133586 7. ) 4. 22 x 102 422 8. ) 8. 96 x 103 8, 960

Computing in Scientific Notation • Example: 0. 0000006 x 32, 000 x 0. 0043 • Step 1 - Write the numbers in Scientific Notation. 6 x 10 -7 x 3. 2 x 107 x 4. 3 x 10 -3 • Step 2 - Use the commutative property to change the order of the factors. 6 x 3. 2 x 4. 3 x 10 -7 x 10 -3.

6 x 3. 2 x 4. 3 x 10 -7 x 10 -3. • Step 3 - Complete the multiplication, using the rule for multiplying with exponents. 6 x 3. 2 x 4. 3 = 82. 56 10 -7 x 10 -3 = 10(-7 + -3) =10 -3 Answer: 82. 56 x 10 -3 • Step 4 - Write the product in scientific notation. 82. 56 x 10 -3= 8. 256 x 10(-3+1)= Answer: 8. 256 x 10 -2

YOUR TURN 1. ) 0. 00645 x 0. 00004302 x 0. 000000035 2. ) (11, 000)2

TO FIND THE QUOTIENT: 9, 250, 000 divided by 25, 000 • Step 1 - Write each number in scientific notation. • 9. 25 x 106 2. 5 x 104 • Step 2 - Rewrite the division as a fraction. 9. 25 x 106 2. 5 x 104

9, 250, 000 / 25, 000 • Step 3 - Complete the division, using the rule for dividing with exponents. 9. 25 x 106 = 3. 7 x 102 2. 5 x 104 2. 5 104 • Step 4 - Check that the product is written in scientific notation. 3. 7 x 102

YOUR TURN • 1. ) 350, 000 divided by 1, 400, 000

Answer 350, 000 / 1, 400, 000 1. ) 3. 5 x 105 / 1. 4 x 106 2. ) 3. 5 x 105 1. 4 x 106 3. ) 3. 5 x 105 = 2. 5 x 10 -1 1. 4 x 106 1. 4 106 4. ) 2. 5 x 10 -1

Using your calculator to solve Scientific Notation Problems • • • Push MODE Scroll to SCI (scientific notation) 2 nd MODE (Quit) Put number into calculator ENTER E means “time 10 to the power of” Ex. 40, 000 = 4 E 7 = 4 x 107

Scientific Notation Open Ended Question • Consider this multiplication expression. (3. 2 x 104) (3 x 103) a. Set your calculator in scientific notation mode and evaluate this expression. b. Explain how you could do the multiplication above without using a calculator. c. Find the product (2. 1 x 106) (4 x 105) and write it in scientific notation.