1. SCIENTIFIC NOTATION

2. In science, we deal with some very LARGE numbers: 1 mole = 602000000000000000000000 In science, we deal with some very SMALL numbers: Mass of an electron = 0.000000000000000000000000000000091 kg Scientific Notation

3. Imagine the difficulty of calculating the mass of 1 mole of electrons! 0.000000000000000000000000000000091 kg x 602000000000000000000000 ???????????????????????????????????

4. Scientific Notation: A method of representing very large or very small numbers in the form: M x 10 n  M is a number between 1 and 10  n is an integer

5. 2 500 000 000 Step #1: Insert an understood decimal point. Step #2: Decide where the decimal must end up so that one number is to its left Step #3: Count how many places you bounce the decimal point 1234567 8 9 Step #4: Re-write in the form M x 10 n

6. 2.5 x 10 9 The exponent is the number of places we moved the decimal.

7. 0.0000579 Step #2: Decide where the decimal must end up so that one number is to its left Step #3: Count how many places you bounce the decimal point Step #4: Re-write in the form M x 10 n 12345

8. 5.79 x 10 -5 The exponent is negative because the number we started with was less than 1.

9. CALCULATORS AND SCIENTIFIC NOTATION  Students have excellent tools to help them solve math and science problems  Effective use these tools takes practice  Calculators are frequently misused, especially with problems requiring scientific notation  Here are some examples

10. SCIENTIFIC NOTATION A balloon is filled with 8.32 g of helium. Calculate the number of atoms of helium in the balloon. Let’s try another problem.

11. SCIENTIFIC NOTATION By one estimate, there are 3 × 10 85 atoms in the universe. How many moles of atoms are in the universe? Did anyone get 5 × 10 107 ? 1 SF

12. SCIENTIFIC NOTATION ERRORS If you did, you may have input the equation as: 3 * 10^85 ÷ 6.022 * 10^23 = 5 × 10 107 Calculators perform multiplication and division from left to right. The calculator performs this operation as: 3 * (10^85) ÷ (6.022) * (10^23 ) = 5 × 10 107

13. SCIENTIFIC NOTATION ERRORS  To keep from getting in trouble, students need to use the “EE” key instead of “*” and “10^”  Parentheses can help, but it’s easy to lose track  3 e 85 means 3 × 10 85  Final answer is 5 x 10 61 NOT 5^61  5^61 = 5 61 = 4 × 10 42

14. p. 34 Scientific Notation Key That EE key is the same as saying “times 10 x ”

15. LOGARITHMS  Many chemistry problems, such as rate laws and pH, use natural and base 10 logarithms  Students have (hopefully) learned about logarithms in their math classes, but unfortunately many may have forgotten  Devoting some class time to algebra and sig figs with logarithms may save trouble later on

16. What is the pH of a 4.79 x 10  5 M solution of HCl? pH =  log (4.79 x 10  5 ) pH = 4.3197 How many SF in the final answer? pH = 4.32 How many SF is this? 3

17. A solution has a pH of 8.91. What is the [H + ]? pH =  log [H + ] = 8.91 (Solve for [H + ]) log [H + ] =  8.91 [H + ] = 10  8.91 [H + ] = 1.230 x 10  9 M Is this our final answer? [H + ] = 1.23 x 10  9 M How many SF is this? 3

18. LOGARITHMS  A radioactive isotope has a half life of 14.3 days. How much of a 175mg sample will remain after 35.0 days?

19. Solve for N t Carry extra digits throughout your calculations. Do not round to the correct number of SF until your final answer.