Introduction: Matter and Measurement Chapter 1

Uncertainty in Measurement The term significant figures refers to digits that were measured. When rounding calculated numbers, we pay attention to significant figures so we do not overstate the accuracy of our answers.

Determining Significant Figures Any digit that is not zero is significant kg 4 significant figures Zeros between nonzero digits are significant 606 m 3 significant figures Zeros to the left of the first nonzero digit are not significant 0.08 L 1 significant figure If a number is greater than 1, then all zeros to the right of the decimal point are significant 2.0 mg 2 significant figures If a number is less than 1, then only the zeros that are at the end and in the middle of the number are significant g 3 significant figures

Rules for Significant Figures Addition or Subtraction The answer cannot have more digits to the right of the decimal point than any of the original numbers round off to 90.4 one significant figure after decimal point two significant figures after decimal point round off to 0.79

Rules for Significant Figures Multiplication or Division The number of significant figures in the result is set by the original number that has the smallest number of significant figures 4.51 x = = sig figsround to 3 sig figs 6.8 ÷ = sig figsround to 2 sig figs = 0.061

Significant Figures Exact Numbers Numbers from definitions or numbers of objects are considered to have an infinite number of significant figures The average of three measured lengths; 6.64, 6.68 and 6.70? Because 3 is an exact number = = 6.67 = 7

Dimensional Analysis We use dimensional analysis to convert one quantity to another. Most commonly dimensional analysis utilizes conversion factors (e.g., 1 in. = 2.54 cm) 1 in cm 1 in. or

Dimensional Analysis Use the form of the conversion factor that puts the desired unit in the numerator. given unit  desired unit desired unit given unit Conversion factor

Dimensional Analysis Method of Solving Problems 1.What data with units are we given in the problem? 2.What quantity and units do we wish to obtain? 3.What conversion factors do we need to take given quantity to desired quantity? 4.If all units cancel except for the desired unit(s), then the problem was solved correctly. 1 L = 1000 mL How many mL are in 1.63 L? 1L 1000 mL 1.63 L x = 1630 mL 1L 1000 mL 1.63 L x = L2L2 mL

The speed of sound in air is about 343 m/s. What is this speed in miles per hour? 1 mi = 1609 m1 min = 60 s1 hour = 60 min 343 m s x 1 mi 1609 m 60 s 1 min x 60 min 1 hour x = 767 mi hour meters to miles seconds to hours

Exercise 1.44 (d) p 33 An individual has 232 mg of cholesterol per 100. mL of blood. If the total blood volume of the individual is 5.2 L, how many total grams of cholesterol does the Individual’s body contain?

Exercise 1.50 p 33 The concentration of carbon monoxide in an urban apartment is 48 μg/m 3. What mass in grams of CO is present in a room measuring 9.0 x 14.5 x 18.8 ft?

In class exercises: Kenyan Daniel Yego won the 2007 Rock ‘N’ Roll Marathon, a 26-mile, 385 yard race, with a time of 2:09:04. At this rate, how long would it take him to run 3.00 miles? A solid sphere of plutonium has a diameter of 10.5 inches. Given that the density of Pu is g/cm 3, what is the mass in kg of the Pu?