1. Significant Figures Revisited Let’s take a look at some instruments used to measure --Remember: the instrument limits how good your measurement is!!

2. Significant figures (sig figs) We can only MEASURE at the lines on the measuring instrument We can only MEASURE at the lines on the measuring instrument We can (and do) always estimate between the smallest marks. We can (and do) always estimate between the smallest marks. 21345 in

3. 4.5 inches What was actually measured? What was estimated? 4 inches 0.5 inches 21345 in

4. Significant figures (sig figs) The better marks… the better we can measure. The better marks… the better we can measure. Also, the closer we can estimate Also, the closer we can estimate 21345 in 21345

5. 21345 4.55 inches What was actually measured? What was estimated? in 4.5 inches 0.05 inches

6. So what does this all mean to you? Whenever you make a measurement, you should be doing three things Whenever you make a measurement, you should be doing three things 1. Check to see what the smallest lines (increments) on the instrument represent 2. Measure as much as you can (to the smallest increment allowed by the device) 3. Estimate one decimal place further than you measured

7. Decimal Places Review 23456.789 thousandths hundredths tenths ones tens hundreds thousands ten thousands Your estimate MUST always be one (and only one) decimal place further to the right than your measurement

8. Practice Your graduated cylinder can only accurately measure to tens of mL. To what decimal place should you estimate? A balance can accurately measure to hundredths of grams. What decimal place will your estimate be?

9. Work Backwards Now Look at the following measurements and determine the smallest increment that the measuring instrument could accurately measure to. Keep in mind that the last significant figure is an estimate. 100.3 g 207 L 1500 cm 0.0004467 kg ones tens thousands One-hundred thousandths

10. What is measured and what is estimated in the following measurements? Remember, only significant figures (digits) are measured or estimated 100.3 207 1500 0.0004467 4 Sig Figs ; Measured: 100. ; Estimated: 0.3 3 Sig Figs ; Measured: 2.0 X 10 2 ; Estimated: 7 2 Sig Figs ; Measured: 1000 ; Estimated: 500 4 Sig Figs ; Measured: 0.000446 ; Estimated: 0.0000007