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Scientific Notation

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

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Scientific Notation

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  1. Scientific Notation When would someone think of using scientific notation?

  2. 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.

  3. How to write in Scientific Notation • Get your number to be between 1 and 9 by moving the decimal to the left or right. • 1,624,000,000,000,000 changes to 1.624000000000000

  4. How Many Spaces? • Count the number of spaces from the beginning decimal point to the new point. • Ex. 1.624,000,000,000,000 (15 spaces)

  5. Moving the Decimal Point • Copy all the whole numbers with the new decimal point : 1.624

  6. Power of Ten • Multiply the remaining number by 10 raised to the number of places the decimal point moved. • 1.624 x 1015

  7. 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

  8. 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.

  9. Your Turn • 1.) 29,900 5.) 222.6 • 2.) 0.0000000033 6.) 2,230,000 • 3.) 883 7.) 0.0000002 • 4.) 0.0199 8.) 17,250

  10. Answers 1.) 29,900 5.) 222.6 2.99 x 104 2.226 x 102 2.) 0.0000000033 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

  11. 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

  12. 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

  13. 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

  14. ANSWERS • 1.) 2.27 x 10-2 5.) 1.33586(105) 0.0227 133,586. • 2.) 3.772 x 104 6.) 1.33586(10-5) 37,720 0.0000133586 • 3.) 5.6 X 10-1 7.) 4.22 x 102 0.56 422 • 4.) 9.7 x 107 8.) 8.96 x 103 97,000,000 8,960

  15. Computing in Scientific Notation • Example: 0.0000006 x 32,000,000 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 x107 x10-3.

  16. 6 x 3.2 x 4.3 x 10-7 x107 x10-3. • Step 3- Complete the multiplication, using the rule for multiplying with exponents. 6 x 3.2 x 4.3 = 82.56 10-7 x107 x10-3 = 10(-7 + 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

  17. YOUR TURN 1.) 0.00645 x 0.00004302 x 0.000000035 2.) (11,000,000)2

  18. 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

  19. 9,250,000 / 25,000 • Step 3- Complete the division, using the rule for dividing with exponents. 9.25 x 106 = 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

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

  21. 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 = 3.5 x 105 = 2.5 x 10-1 1.4 x 106 1.4 106 4.) 2.5 x 10-1

  22. Using your calculator to solve Scientific Notation Problems • Push MODE • Scroll to SCI (scientific notation) • 2nd MODE (Quit) • Put number into calculator ENTER • E means “time 10 to the power of” • Ex. 40,000,000 = 4E7 = 4 x 107

  23. Scientific Notation Open Ended Question • Consider this multiplication expression. (3.2 x 104) (3 x 103) • Set your calculator in scientific notation mode and evaluate this expression. • Explain how you could do the multiplication above without using a calculator. • Find the product (2.1 x 106) (4 x 105) and write it in scientific notation.

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