1. Operations with Scientific Notation

2. Addition and Subtraction Format Addition (N * 10 x ) + (M * 10 x ) = (N + M) * 10 x Subtraction (N * 10 y ) - (M * 10 y ) = (N-M) * 10 y

3. Different Scenarios When we add or subtract using scientific notation, we encounter two scenarios: 1. Same power of ten Ex. (3 x 10 3 ) + (5 x 10 3 ) 2. Different powers of ten Ex. (2 x 10 4 ) – (8.3 x 10 6 )

4. Same Power of Ten When we have the same power of ten 1.Add/subtract the bases 2.Attach the power of ten 2.56 x 10 3 + 6.964 x 10 3 Add the Bases: 2.56 + 6.964 = 9.524 Attach the power of ten: 9.524 x 10 3

5. Same Powers of Ten Example: Subtraction 9.49 x 10 5 – 4.863 x 10 5 Subtract bases: 9.49 – 4.863 = 4.627 Attach power of ten: 4.627 x 10 5

6. You Try! 9.0979 x 10 3 - 3.252 x 10 3 = 6.95 x 10 4 - 9.94 x 10 4 = 3.261 x 10 7 + 8.294 x 10 7 = 3.262 x 10 5 + 2.892 x 10 5 = 5.8459 x 10 3 -2.99 x 10 4 11.555 x 10 7 = 1.1555 x 10 8 6.154 x 10 5

7. Different Powers of Ten We must have the same power of ten in order to add or subtract! If the powers are different, you must move the decimal either right or left (on one of the numbers) so that they will have the same exponent.

8. Moving the Decimal For each move of the decimal to the right you have to add -1 to the exponent. For each move of the decimal to the left you have to add +1 to the exponent.

9. Different Powers of Ten 2.46 x 10 6 + 3.476 x 10 3 If I want to make 10 3 into 10 6 I have to shift the decimal 3 places to the left. (add 3 to the exponent) 0.003476 x 10 3+3 2.46 x 10 6 + 0.003476 x 10 6 Answer: 2.463 x 10 6

10. Different Powers of Ten 5.762 x 10 3 – 2.65 x 10 -1 If we want to turn 10 -1 into 10 3 we have to move the decimal 4 places to the left (add 4 to the exponent) 0.000265 x 10 (-1+4) 5.762 x 10 3 -0.000265 x10 3 Answer: 5.762 x 10 3

11. You Try! 2.3545 x 10 1 + 3.602 x 10 2 = 3.9261 x 10 2 + 1.5238 x 10 3 = 3.2641 x 10 1 + 8.2294 x 10 4 = 3.2005 x 10 2 - 4.527 x 10 1 = 3.8375 x 10 2 1.9164 x 10 3 8.2327 x 10 4 2.7478 x 10 2

12. Rounding With Scientific Notation When we write scientific notation, we often round to the nearest hundredth. Ex. 3.4563 x 10 6  3.46 x 10 6 When we convert a rounded number to standard form, all of the digits after the ones we are given are written as zero. Ex. 3.4563 x 10 6 = 3,456,300 3.46 x 10 6 = 3,460,000

13. You Try! Round to the nearest hundredth, then convert to standard form. 1.9164 x 10 7 8.2671 x 10 12 5.8456 x 10 -2

14. Multiplication and Division To multiply or divide, we use our laws of exponents! Multiplication: 1.Multiply the bases 2.Add the powers of ten Division: 1.Divide the bases 2.Subtract the exponents

15. Examples (2.36 x 10 2 ) * (3.564 x 10 3 ) 2.36 * 3.564 = 8.41104 2 +3 = 5 8.41104 x 10 5  8.41 x 10 5 (12.36 x 10 2 ) ÷ (3.563 x 10 3 ) 12.36 ÷ 3.563 = 3.468986809 2 - 3 = -1 3.468986809 x 10 -1  3.47 x 10 -1