Scientific Notation

1. Scientific Notation

2. Why use Scientific Notation? 602,200,000,000,000,000,000,000 atoms 6.022 x 1023 atoms 0.000 000 000 000 000 000 000 000 000 9109 g 9.109 x 10-28 g

3. M x 10n M is coefficient 1 ≤ M < 10 has only one nonzero digit in front of decimal n is exponent integer (…, -3, -2, -1, 0, 1, 2, 3, …) + exponent  number greater than 1 (larger) - exponent  number less than 1 (smaller)

4. Practice Express the following numbers in correct scientific notation. 1) 0.0005 2) 8,970,000 3) 400 4) 60 5) 0.035

5. Practice Convert the following numbers into extended (standard) notation. 6) 8 x 101 7) 4.56 x 10-5 8) 5.400 x 105 9) 8 x 10-3 10) 6.000 x 102

6. Remember….Rules for Sig Figs: All digits written in the coefficient of a number in scientific notation are significant. Example: 1.00 x 105 has 3 sig figs 1 x 10-3 has 1 sig fig

7. Operations with Scientific Notation • Multiplication • Multiply coefficients. • Add exponents. • Re-express answer in correct scientific notation, if needed. • Round answer to the correct number of sig figs placed on the rule for multiplying.

8. Operations with Scientific Notation • Division • Divide coefficients. • Subtract exponents. • Re-express answer in correct scientific notation, if needed. • Round answer to the correct number of sig figs placed on the rule for dividing.

9. Operations with Scientific Notation • Addition/Subtraction • Exponents must be same; if not, change one number to match the other exponent. (choose the larger exponent) • Add/subtract coefficients; keep exponents same. • Re-express answer in correct scientific notation, if needed. • Sig figs (tough because based on decimal places)