Numbers are central to Science You can not “do” Chemistry without basic numerical skills. Measurement and error: Every measurement except for counting the measured value contains some type of inherent error.

Error Types Random Error: Error that occurs randomly and that normally cannot be avoided. There is an equal probability of a + and a - deviation from the measured value. Systematic or Determinate Error: A type of error with both a definite magnitude and sign. Typical sources are Instrumental errors and Method errors.

Accuracy: • Indicates how close a measured value is to the true value Accuracy: • Indicates how close a measured value is to the true value. • Effected by both random and systematic error. • Determined from a comparison of average measured values with known values. Precision: • A measure of the reproducibility of the method. • How close are the results obtained in the same way? • Determined from a comparison of measured values with the average measured value. • Standard deviation is an effective monitor of random error.

Figure: 01-11-04UN Title: Accuracy, precision, and significant figures Caption: The balance on the left has a low or poor precision than the balance on the right (which has high or good precision). The number of reported significant figures often indicates this - it would be senseless to report to a number of decimals that cannot be trusted due to low precision. Notes:

Significant Figures There are two types of numbers; Counting numbers: Counting Numbers are exact, i.e. 30 students in Chem. 121. Measured numbers: Measured numbers have units and significant figures. Significant figures reflect the magnitude of certainty or the precision of the measurement.

Figure: 01-12 Title: Determining the number of significant figures in a quantity Caption: The quantity shown here, 0.004004500, has seven significant figures. All nonzero digits are significant, as are the indicated zeros. Scientific notation allows one to see just the significant figures (4.004500 x 10-3). Notes:

For a measurement, the number should include all digits known with certainty and the first uncertain digit. For single measurements, the first digit for which you are uncertain is generally the one resulting from estimating to 1/10th of the smallest scale division.

For example… If one is measuring the diameter of a coin using a ruler with the smallest divisions being in increments of 1 mm, the measurement is made to the nearest 1/10th of a millimeter or 0.1 mm.

If an object is said to be 23 If an object is said to be 23.5 mm long, then the certainty of the measurement is also evident. i.e., between 23.4 and 23.6 inches. The final digit, “5" is estimated and has some uncertainty associated with it. The value 24.5 has 3 significant digits. Writing the measurement as 2 cm (1 sig. fig.) or 24 mm (2 sig. figs.), or 24.00 (4 sig. fig.) mm is not correct in that it does not convey the precision of the measurement.

How many significant figures are in; (a) 23 inches (b) 0.045 mm (c) 60001 Liters (d) 6 people (e) 0.00100 miles (f) 100 Km

Significant Figures (Functions) Addition & Subtraction : same digits after decimal as least Multiplication & Division: same number of sig. figs. as least • 2.8 x 4.5039 = 12.61092 → round to 13 • (6.85) ÷(112.04) = 0.0611388789→round to 0.0611 (6.11 x 10-2)

1-4 The Measurement of Matter Copyright © 2011 Pearson Canada Inc. General Chemistry: Chapter 1

General Chemistry: Chapter 1 Copyright © 2011 Pearson Canada Inc.

General Chemistry: Chapter 1 Mass Mass is the quantity of matter in an object. Weight is the force of gravity on an object W α m W = g × m Copyright © 2011 Pearson Canada Inc. General Chemistry: Chapter 1

General Chemistry: Chapter 1 Volume Copyright © 2011 Pearson Canada Inc. General Chemistry: Chapter 1

SI and non-SI Units Compared 1 Imperial qt 1.136 L 1 US qt 0.936 L 1 L 1 kg 1 lb 1 in 1 cm Copyright © 2011 Pearson Canada Inc. General Chemistry: Chapter 1

Density in Conversion Pathways What is the mass of a cube of osmium that is 1.25 inches on each side? Have volume, need density = 22.59g/cm3 Copyright © 2011 Pearson Canada Inc. General Chemistry: Chapter 1

Problem Solving (Dimensional Analysis): All measured numbers must have units to carry any meaning. The careful consideration of these units (the dimensions) can provide insight into problem solving. For example; You know you live 3.0 miles away from a mall. Can you determine how many feet you are from the mall, given there are 5280 feet in a mile? 3.0 mile x 5280 feet/mile = 15840 feet = 1.6 x 104 feet

Problem Solving Recipe: 1. Write down the given number(s) with its units. 2. Write a ratio with the given number in the denominator (at the bottom) and the unit sought in the numerator (on top). 3. Insert numbers into the ratio such that numerator and denominator are equal. 4. Multiply Steps 1 and 3 together.