2. Sig Figs Significant Figures

3. What are Sig Figs?  I read in the paper that Randy Lerner (owner of the Browns) is worth 1.7 billion dollars.  Myself and a friend bought 4 tickets for $264.30  Assume Randy Lerner gets every penny of that and hasn’t had another expense yet, does that mean Randy Lerner now has exactly $1,700,000,264.30?  Of course not, all of those 0’s were actually numbers that we didn’t report because we couldn’t measure accurately enough. The number was rounded!

4. This is where sig figs come into play  Absolutely accurate measurements are impossible!!!  We must round somewhere  When we do calculations with these numbers we must reflect how accurate our initial numbers were.  A significant digit means that digit was accurately measured  An Insignificant digit means that digit was NOT accurately measured.

5. Rules for determining if a digit is significant 1. If it is not a zero, it is significant.123 2. If a zero is between two significant digits, it is significant. 309 3. Zeros at the end of a number with a decimal point are significant. 56.0 4. Zeros at the end of a number that do not have a decimal point are NOT significant. 82400 5. Zeros at the front of a decimal are NOT significant..00562

6. Determine how many sig figs are in each number  734  100,025  6501000 .00034  2.00034  527.00  16.01  18700000000000 3333 6666 4444 2222 6666 5555 4444 3333

7. Round each number to the given number of sig figs  (2) 734  (4) 101.025  (3) 651500  (5).00334  (4) 132.084  (3) 527.00  (5) 16.01  (3) 18700  730  101.0  652000 .0033400  132.1  527  16.010  18700

8. How to report answers  When multiplying or dividing.  You can only have as many sig figs in your answer as you do in the number with the least amount of sig figs.  3.56 x 2.1=  7.476  7.5 (2 sig figs)  When adding or subtracting.  Numbers added to or subtracted from insignificant numbers are insignificant (rounded off).  347.58 + 21  368.58  369 insignificant

9. Scientific Notation  some numbers so large or small that is a pain to write out normally  for example $1,700,000,000  To write in scientific notation write down all sig figs x10 x  The number is always written to the ones place with a decimal  The number it is raised to is the number of places you need to move to the decimal.  so the above number is $1.7x10 9

10. Quick conversions  6.7 x10 -7  2.31 x10 5  5.79 x10 3  4.19 x10 -5 .0065  94,100,000 .000000065  9,840 .00000067  231000  5790 .0000419  6.5 x10 -3  9.41 x10 7  6.5 x10 -8  9.84 x10 3