Numbers From Measurements

Measurement Types of Measurement Measurement is a quantitative observation which can be described as the determination of dimensions, capacity, quantity or extent of something Types of Measurement Mass Volume Concentration Temprature Time Pressure

Categories of Numbers Exact Number: number that has a value with no uncertainty in it. E.g a dozen is 12 and gross is 144. Inexact Number: number that has a value with a degree of uncertainty in it. It is impossible to make an exact measuremnt due to defect in measuring device or improper calibration which introduces some uncertainty.

Precision and Accuracy Accuracy: Agreement of a particular value with the true value. Precision: Degree of agreement among several measurements of the same quantity. In throwing darts, precision refers to how close the darts are to each other. High precision and lowAccuracy?

Error (Imperfection) Errors can either be Systematic error: is a constant error associated with an experimental system itself. E.g improper calibration of equipment. A random error: caused by uncontrollable variables in an experiment. E.g momentary changes in temperature near a sensitive instrument. Accurate measurement have low systematic and random error. Accurate measurement is however possible with high random error based on averaging if the highs and lows balance each other.

Concept Check A lab technician was assigned the task of determining the pH of a sample of blood. The technician performed three replicate measurements of the pH and reported the following results. pH = 6.98 pH = 6.99 pH = 6.98 The actual pH of blood is 7.40. Evaluate the technician's job performance in terms of accuracy and precision Precise but not accurate

Uncertainty in Measurement Measurement of Volume Using a Buret The volume is read at the bottom of the liquid curve (meniscus). Meniscus of the liquid occurs at about 20.15 mL. Certain digits: 20.15 Uncertain digit: 20.15 The most common origin of uncertainty in a measurement are Human error and Instrument error.

Rules for Counting Significant Figures (a) Zero Integers (b) Non zero Integers. (a) Nonzero integers always count as significant figures. 3456 has 4 sig figs (significant figures).

9.300 has 4 sig figs. 150 has 2 sig figs. 0.048 has 2 sig figs There are three classes of zeros. a. Leading zeros are zeros that precede all the nonzero digits. These do not count as significant figures. 0.048 has 2 sig figs b. Captive zeros are zeros between nonzero digits. These always count as significant figures. 16.07 has 4 sig figs. c. Trailing zeros are zeros at the right end of the number. They are significant only if the number contains a decimal point. 9.300 has 4 sig figs. 150 has 2 sig figs.

Exponential Notation 1 inch = 2.54 cm, exactly. 3. Exact numbers have an infinite number of significant figures. 1 inch = 2.54 cm, exactly. 9 pencils (obtained by counting). Exponential Notation Example 300. written as 3.00 × 102 Contains three significant figures. Two Advantages Number of significant figures can be easily indicated. Fewer zeros are needed to write a very large or very small number.

Significant Figures in Mathematical Operations For multiplication or division, the number of significant figures in the result is the same as the number in the least precise measurement used in the calculation. Example 1.342 × 5.5 = 7.381  7.4

2. For addition or subtraction, the result has the same number of decimal places as the least precise measurement used in the calculation.