1. SIGNIFICANT FIGURES

2. ACCURACY VS. PRECISION  In labs, we are concerned by how “correct” our measurements are  They can be accurate and precise  Accurate: How close a measured value is to the actual measurement  Precise: How close a series of measurements are to each other

3. EXAMPLE  The true value of a measurement is 23.255 mL  Below are a 2 sets of data. Which one is precise and which is accurate? 1. 23.300, 23.275, 23.235 2. 22.986, 22.987, 22.987

4. SCIENTIFIC INSTRUMENTS  In lab, we want our measurements to be as precise and accurate as possible  For precision, we make sure we calibrate equipment and take careful measurements  For accuracy, we need a way to determine how close our instrument can get to the actual value

5. SIGNFICANT FIGURES  We need significant figures to tell us how accurate our measurements are  The more accurate, the closer to the actual value  Look at this data. Which is more accurate? Why?  25 cm  25.2 cm  25.22 cm

6. ANSWER  25.22cm  The more numbers past the decimal (the more significant figures ), the closer you get to the true value.  How do we determine how many significant figures are in different pieces of lab equipment?

7. SIGNIFICANT FIGURES  Significant figure – any digit in a measurement that is known for sure plus one final digit, which is an estimate  Example:  4.12 cm  This number has 3 significant figures  The 4 and 1 are known for certain  The 2 is an estimate

8. SIGNIFICANT FIGURES  In general: the more significant figures you have, the more accurate the measurement  Determining significant figures with instrumentation  Find the mark for the known measurements  Estimate the last number between marks

9. SIGNIFICANT FIGURES  Try these:  Graduated cylinder  Triple Beam balance  Ruler

10. RULES FOR SIGNIFICANT FIGURES  Rule 1: Nonzero digits are always significant  Rule 2: Zeros between nonzero digits are significant  40.7 (3 sig figs.)  87009 (5 sig figs.)  Rule 3: Zeros in front of nonzero digits are not significant  0.009587 (4 sig figs.)  0.0009 (1 sig figs.)

11. RULES FOR SIGNIFICANT FIGURES  Rule 4: Zeros at the end of a number and to the right of the decimal point are significant  85.00 (4 sig figs.)  9.070000000 (10 sig figs.)  Rule 5: Zeros at the end of a number are not significant if there is no decimal  40,000,000 (1 sig fig)

12. RULES FOR SIGNIFICANT FIGURES  Rule 6: When looking at numbers in scientific notation, only look at the number part (not the exponent part)  3.33 x 10 -5 (3 sig fig)  4 x 10 8 (1 sig fig)  Rule 7: When converting from one unit to the next keep the same number of sig. figs.  3.5 km (2 sig figs.) = 3.5 x 10 3 m (2 sig figs.)

13. HOW MANY SIGNIFICANT FIGURES? 1. 35.02 2. 0.0900 3. 20.00 4. 3.02 X 10 4 5. 4000

14. ANSWERS 1. 4 2. 3 3. 4 4. 3 5. 1

15. ROUNDING TO THE CORRECT NUMBER OF SIG FIGS.  Many times, you need to put a number into the correct number of sig figs.  This means you will have to round the number  EXAMPLE:  You start with 998,567,000  Give this number in 3 sig figs.

16. ANSWER  Step 1: Get the first 3 numbers (3 sig figs.)  998  Step 2: Check to see if you have to round up or keep the number the same  You need to look at the 4 th number  998 5  If the next number is 5 or higher, round up  If the next number is 4 or less, stays the same  Therefore = 999

17. ANSWER  Step 3: Take your numbers and put the decimal after the first digit  9.99  Step 4: Count the number of places you have to move to get to the end of the number and put it in scientific notation.  9.99 x 10 8  NOTE: If the number is BIG it will be a positive exponent. If the number is a DECIMAL, it will be a negative exponent.

18. OTHER POSSIBILITY  Example:  999,999,999 (3 sig. figs.)  When you take the first three numbers, you get  999  But when you round, it is going to round from 999  1000  Therefore, the number becomes:  1.00 x 10 8

19. TRY THESE 1. 10,000 (3 sig. figs.) 2. 0.00003231 (2 sig. figs.) 3. 347,504,221 (3 sig. figs.) 4. 0.000003 (2 sig. figs.) 5. 89,165,987 (3 sig. figs.)