1. Regents Chemistry Scientific Notation PowerPoint Lectures Notes

2. Add/Subtract with identical exponents S.N. expressed in the form of M x 10 n If the numbers have the same exponent, n, add or subtract the values of M and keep the same n

3. For example… 3.0 x 10 5 m + 5.0 x 10 5 m = (3 + 5) x 10 5 m = 8.0 x 10 5 m 8.5 x 10 3 kg + 3.6 x 10 3 kg = 12.1 x 10 3 kg

4. Add/Subtract with different exponents If the exponents are not the same, move the decimal point left or right until they are the same. Then add or subtract M. How do we do this???

5. Dealing with positive exponents 3.0 x 10 5 also equals 300,000 300,000 number gets larger, so we need less of a positive exponent to make an equal value number gets smaller, so we need more of a positive exponent to make an equal value 0.30 x 10 6 30.0 x 10 4 Count the moves and see!

6. Dealing with negative exponents 3.0 x 10 -5 also equals 0.00003 0.00003 number gets larger, so we need less of a negative exponent to make an equal value We are moving closer to the decimal point! 0.30 x 10 -4 number gets smaller, so we need more of a negative exponent to make an equal value. We are moving further from the decimal point! 30.0 x 10 -6 Count the moves and see! 0.00003

7. Practice Problems 1.5 x 10 3 = 0.15 x 10 ? 2.0 x 10 5 = 200 x 10 ? 3.6 x 10 -3 = 0.36 x 10 ? 5.5 x 10 -5 = 5500 x 10 ? 0.15 x 10 4 200 x 10 3 0.36 x 10 -2 5500 x 10 -8

8. Multiplying with S.N. (2.0 x 10 2 ) (3.0 x 10 3 ) = Multiply the values of M Add exponents Multiply units (2.0) (3.0) = 6.0 x 10 2+3 = 6.0 x 10 5

9. Multiplying with S.N. When products are larger than 9.9999 (5.0 x 10 3 ) (6.0 x 10 4 ) = (5.0 x 6.0) = 30 x 10 3+4 = 30 x 10 7 But is this proper form? 3.0 x 10 8

10. Dividing with S.N. 6.0 x 10 5 2.0 x 10 2 Divide the values of M Subtract exponents 6.0 / 2.0 = 3.0 x 10 5-2 = 3.0 x 10 3 Practice: 10.0 x 10 5 5.0 x 10 6

11. Practice Problems (6.0 x 10 5 ) (3.0 x 10 4 ) = (4.0 x 10 3 ) (7.0 x 10 8 ) = (1.0 x 10 2 ) (2.0 x 10 -4 ) = 6.0 x 10 8 2.0 x 10 4 = 18.0 x 10 9 28.0 x 10 11 2.0 x 10 -2 3.0 x 10 4