Presentation on theme: "Honors Chemistry I. Uncertainty in Measurement A digit that must be estimated is called uncertain. A measurement always has some degree of uncertainty."— Presentation transcript:
Uncertainty in Measurement A digit that must be estimated is called uncertain. A measurement always has some degree of uncertainty.
Why Is there Uncertainty? Measurements are performed with instruments. No instrument can read to an infinite number of decimal places Which of these balances has the greatest uncertainty in measurement?
Precision and Accuracy Accuracy refers to the agreement of a particular value with the true value. Precision refers to the degree of agreement among several measurements made in the same manner. Neither accurate nor precise Precise but not accurate Precise and accurate
Types of error Random Error (indeterminate Error) – measurement has an equal probability of being high or low. Systematic Error ( Determinate Error) – Occurs in the same direction each time (high or low), often resulting from poor technique or incorrect calibration.
Percent error % error = |experimental value – theoretical value| x 100% theoretical value
Rules for Counting Significant Figures Nonzero integers- Every nonzero digit in a reported measurement is assumed to be significant. 3456 has 4 significant figures
Rules for Counting Significant Figures Zeros Leading zeros do not count as significant figures. They act as placeholders. By writing the measurements in scientific notation, you can eliminate such place holding zeros. 0.0486 has 3 significant figures 0.000099 has 2 significant figures
Rules for Counting Significant Figures Zeros Sandwiched zeros : ( zeros appearing between nonzero digits) always count as significant figures. 16.07 has 4 significant figures 7003 has 4 significant figures
Rules for Counting Significant Figures Zeros Trailing zeros are significant only if the number contains a decimal point. 300 meters has 1 significant figure 7000 has 1 significant figure 27,210 has Four significant figures
Zeros at the end of a number and to the right of a decimal point are always significant. 43.00 has Four significant figures 1.010 has 4 significant figures 9.000 has 4 significant figures
Exact numbers have an infinite number of significant figures. There are two situations in which numbers have an unlimited number of significant figures. 1. Counting, a number that is counted is exact. Ex. 28 people in your classroom- 2 significant figures. 2. The second situation involves exactly defined quantities such as those found within a system of measurement. Ex. 60 min = 1 hr – unlimited number of significant figures 100 cm = 1 m – unlimited number of significant figures
Sig fig Practice # 1 How many significant figures in each of the following? 1.0070 m ---- 5 sig figs 17.10 kg ----- 4 sig figs 100,890 L -- 5 sig figs 3.29 x 10^3 s -- 3 sig figs 0.0054 cm -- 2 sig figs 3,200,000 - 2 sig figs
Rules for significant figures in mathematical operations Multiplication and Division – number of significant figures you need to round the answer to the same number of significant figures as the measurement with the least number of significant figures. The position of the decimal point has nothing to do with the rounding process when multiplying and dividing measurements. Ex. 6.38 x 2.0 = 12.76 - 13 (2 significant figures)
Rules for significant figures in mathematical operations Addition and Subtraction: The answer to an addition or subtraction calculation should be rounded to the same number of decimal places (not digits) as the measurement with the least number of decimal places. 6.8 + 11.934= 18.734 18.7 ( 3 sig figs)