Which tool on the left could you be the most precise with? 1.3 Notes Continued… buret How does the precision of measurements affect the precision of scientific calculations? Which tool on the left could you be the most precise with? Graduated cylinder buret

Limits of Measurement Precision Precision is a gauge of how __________ a measurement is. Which clock is the most precise…how can you tell? exact Digital clock – measuring with more digits!

Limits of Measurement The digits involved in your measurement are called __________________ __________________ (sig figs) Sig figs are all the digits that are __________ in a measurement, plus the last digit that is _______________. significant figures known estimated

The number of significant digits depends on how the measuring device is calibrated… The first meter stick can report _____ sig fig The second meter stick can report _____ sig figs The third meter stick can report _______ sig figs 1 2 3

Sig fig Rules All nonzero digit are considered significant figures… 576 meters = Zeros in between nonzero digits are considered significant figures… 5007 meters = Zeros that aren’t shown when a number is in scientific notation do not count as sig figs 5000 meters = 5 x 103 meters = 0.00072 meters = 7.2 x 10-4 meters= 3 sig figs 4 sig figs 1 sig fig 2 sig fig

Sig fig Rules Zeros at the end of a number with a __________ are there because they were measured…they count as sig figs Example: You measured 50.0 meters exactly, as opposed to 50.1 meters 50.0 meters = 5.00 x 101 meters = decimal 3 sig figs

Limits of Measurement The precision of a calculated answer is limited by the _____________ precise measurement used in the calculation. least Calculated answer

Limits of Measurement Mass = 34.73 grams (sig figs? ) 4 Volume = 4.42 cubic centimeters (sig figs? ) If the least precise measurement in a calculation has three significant figures, then the calculated answer can only have at most _________ significant figures. After rounding, our final answer is… 4 3 three Use this 7 to round Calculated answer Least precise measurement 7.86 g/cm3

Limits of Measurement The same applies for adding and subtracting.. Students measured two masses using two different tools… 1.52 grams (sig figs? ) 1.8 grams (sig figs? ) What is the total mass? This should be rounded to… 1.52 g _+1.8__g 3.32 g (calculated answer) After rounding, our final answer is… 3 2 Least precise measurement 3.3 g

Limits of Measurement Accuracy Another important quality in a measurement is its accuracy. Accuracy is the ______________ of a measurement to the expected or __________ value of what is being measured. For example, suppose a digital clock is running 15 minutes ___________. Although the clock would remain precise to the nearest second, the time displayed would not be accurate. closeness true ahead

If the bull’s-eye represents the true value, which dart board represents higher accuracy? On the left – closer to target

Measuring Temperature A ___________________ is an instrument that measures temperature, or how hot an object is. thermometer At what temperature on the celsius scale does…. water boil? water freeze? At what temperature on the kelvin scale does… 100°C 0°C 373 K 273 K

Practice: Convert 15 °C to kelvin So both the Kelvin and Celsius scales have _______ divisions between water’s boiling and freezing point 100 °C = K - 273 K = °C + 273 Practice: Convert 15 °C to kelvin K = 15°C + 273 = 288 K

Assessment Questions A student measures the volume and mass of a liquid. The volume is 50.0 mL and the mass is 78.43 g. What is the correct calculated value of the liquid’s density? (A calculator reads 1.5686.) 1.6 g/cm3 1.57 g/cm3 1.569 g/cm3 1.5686 g/cm3

Assessment Questions 2. What is the difference between precision and accuracy? How exact a measurement is How close the measurement is to the true value

3. How can you convert the temperature of 32 °C to kelvin? Assessment Questions 3. How can you convert the temperature of 32 °C to kelvin? add 32 subtract 32 add 273 subtract 273