CH. 2 - MEASUREMENT I. Using Measurements

A. Accuracy vs. Precision Accuracy - how close a measurement is to the accepted value Precision - how close a series of measurements are to each other ACCURATE = CORRECT PRECISE = CONSISTENT

Accuracy vs. Precision Even the most carefully taken measurements are always inexact. This can be a consequence of inaccurately calibrated instruments (rulers, graduated cylinder, human error, or any number of other factors. Two terms are used to describe the quality of measurements: and PRECISION ACCURACY

What is ? PRECISION ACCURACY Precision is a measure of how closely individual measurements agree with one another. Accuracy refers to how closely individually measured numbers agree with the correct or "true" value.

Precision: these measurements agree with one another. Accuracy: these numbers agree with the correct or "true" value.

What is the uncertain digit? The number 83.4 has three digits. All three digits are significant. The and the are “ digits" while the 4 is the “ digit." As written, this number implies uncertainty of plus or minus 0.1, or error of 1 part in 834. 8 3 certain estimated

79.85 Most certain number Least certain number Which number is least certain and an estimate? Which number is most certain and accurate? Most certain number Least certain number

B. Percent Error your value accepted value Indicates accuracy of a measurement your value accepted value

B. Percent Error % error = 2.9 % A student determines the density of a substance to be 1.40 g/mL. Find the % error if the accepted value of the density is 1.36 g/mL. % error = 2.9 %

C. Significant Figures Indicate precision of a measurement. Recording Sig Figs Sig figs in a measurement include the known digits plus a final estimated digit 2.35 cm

C. Significant Figures Counting Sig Figs Count all numbers EXCEPT: Leading zeros -- 0.0025 Trailing zeros without a decimal point -- 2,500

All non zero numbers are significant Ex: 96, 22223, 3.21X108 Zeros between non zero digits are significant 101, 10000202220002, 3.0201X108 Zeros at the end of a number that include a decimal are significant 101.000, 222.0, 100.00, 3.0X108

The Atlantic Pacific Rule Simplified Sig Figs The Atlantic Pacific Rule The “A” in Atlantic represents the absence of a decimal in a number. The “P” in Pacific represent the presence of a decimal in a number. Pacific Ocean Decimal Present Atlantic Ocean Decimal Absent

Atlantic Pacific Rule To use this rule we must 1st understand what a “non-zero” digit is. Digits are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. These digits are used in many combinations to create what we call numbers. A “non zero” digit is any digit other than 0. 1, 2, 3, 4, 5, 6, 7, 8, 9, these are all “non zero” digits.

In the number 12.01 is the decimal present or absent? So we start from the Pacific side of the U.S. Then we travel from the Pacific to the Atlantic counting digits along the way. We begin counting digits at the 1st “non-zero” digit, and count it and every digit (even zeros) that follows. So we count this number and every digit that follows toward the Atlantic. Is this digit a “non-zero” digit? yes 1 2. 1 Therefore, the number 12.01 has 4 significant digits.

In the number 1,200 is the decimal present or absent? So we start from the Atlantic side of the number. Yes, we count this digit and every digit that follows toward the Pacific. Is this a “non-zero” digit? Then we travel from the Atlantic to the Pacific counting digits along the way. We begin counting digits at the 1st “non-zero” digit, and count it and every digit (even zeros) that follows. Do we count this digit? no yes 1 2 Therefore, the number 1,200 has only 2 significant digits.

Counting Sig Fig Examples C. Significant Figures Counting Sig Fig Examples 1. 23.50 1. 23.50 2. 402 2. 402 3. 5,280 3. 5,280 4. 0.080 4. 0.080

C. Significant Figures (13.91g/cm3)(23.3cm3) = Calculating with Sig Figs Multiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer. (13.91g/cm3)(23.3cm3) = 4 SF 3 SF

C. Significant Figures 3.75 mL + 4.1 mL 3.75 mL + 4.1 mL 224 g + 130 g Calculating with Sig Figs (con’t) Add/Subtract - The # with the lowest precision (decimal place) determines the place of the last sig fig in the answer. 3.75 mL + 4.1 mL 3.75 mL + 4.1 mL 224 g + 130 g 224 g + 130 g  

C. Significant Figures Calculating with Sig Figs (con’t) Exact Numbers do not limit the # of sig figs in the answer. Counting numbers: 12 students Exact conversions: 1 m = 100 cm “1” in any conversion: 1 in = 2.54 cm

C. Significant Figures Practice Problems 5. (15.30 g) ÷ (6.4 mL) =  4 SF 2 SF =  2 SF 6. 18.9 g - 0.84 g 