1. 1 matter An experimental science interested in understanding the behavior and composition of matter. measurement Chemistry, as an experimental science, is always involved in the acquisition of data, most of it is the product of a measurement. What Is a Measurement? a quantitative observation a comparison to an agreed-upon standard 0.0004 lb every measurement has a number and a unit 4.5 g 5.082 kg 25.0 ºC 0.0004 lb. CHEMISTRY significant figures it is a statement of accuracy: (very accurate = very close to the real value) Here we use significant figures number + unit scientific notation it is a statement of magnitude: (very small, small, large, very large) Here we use scientific notation

2. 2 scientific notation A number in scientific notation contains a coefficient and a power of 10. 1.5 x 10 2 7.35 x 10 -4 To write a number in scientific notation  Move the decimal point so as to place it after the first non-zero digit. This step makes the coefficient always greater than 1 but less than 10.  The spaces moved and the direction are shown as a power of ten. 4 Positive if moved to the left52 000. = 5.2 x 10 4 4 spaces left -3 Negative if moved to the right0. 00378 = 3.78 x 10 -3 3 spaces right

3. 3 Every measured number has a degree of uncertainty. The more uncertain, the less accurate. Determine the length of the wood.

4. Find the smallest graduation: 1. Find the smallest graduation: Subtract the values of any two adjacent labeled graduations and divide by the number of intervals between them. 3-4 = 1 = 1 cm graduations 1 1 Take the uncertainty to be 10% 2. Take the uncertainty to be 10% of the smallest graduation: To obtain the correct reading: absolute uncertainty We assume that one can measure accurately to one-tenth of the smallest markings = absolute uncertainty 10% of 1 = 0.10 x 1 = 0.1 Therefore your measurement should have: 4 1 decimal place 4.7 4.7 ± 0.1{ 4.6, 4.7, 4.8 }

5. 5 Follow the steps and determine the length.

6. The first digit 4known plus the second digit 4.5known The third and last digit is obtained by estimating.4.56 Known + estimated number = Significant figures or Significant numbers 3 4.56 has 3 significant numbers 6 Summary

7. 7 Zero as a Measured Number 1. Find the smallest graduation: Subtract the values of any two adjacent labeled graduations and divide by the number of intervals between them. 4-3 = 1 = 0.1 cm graduations10 2. Take the uncertainty to be 10% of the smallest graduation: 4.50 cm 10% of 0.1 = 0.10 x 0.1 = 0.01 Therefore your measurement should have 2 decimal places The last digit can be any digit between 0 and 9 in increments of 0.01 Follow the steps and determine the length.

8. Rules to determine significant figures

9. 1.Use a scientific calculator to carry out the following mathematical operations. Provide answers in scientific notation and one decimal place. a.(7.2 x 10 –3 ) (2.4 x 10 5 )b. 2.4 x 10 5 7.2 x 10 –3 Practice 2.State the number of significant figures in each of the following measurements: a. 0.030 mb. 4.050 Lc. 0.0008 gd. 2.80 m 3.Which answer(s) contains 3 significant figures? a) 0.4760b) 0.00476 c) 4.76 x 10 3 4. All the zeros are significant in a) 0.00307 b) 25.300 c) 2.050 x 10 3

10. 5. Follow the steps and obtain a measurement for the solids and liquid. (c) Practice

11. Significant Figures in Calculations 11 can not increase significant figures One can not increase significant figures (reduce the uncertainty) by means of a mathematical operation. 2.73 2.7325471 Calculator This can only be done by the measuring instrument. round-off To remove non-significant numbers one must round-off. Rules for Rounding Off 4 or less If the first digit to be dropped is 4 or less, it and all following digits are dropped. To round 45.832 to 3 significant figures 3 45.8 32drop the digits 32 = 45.8 5 or greater If the first digit to be dropped is 5 or greater, the last retained digit is increased by 1. To round 2.4884 to 2 significant figures 82.5 2.4 884drop the digits 884 and increase the 4 by 1 = 2.5 one or more zeroes are added Sometimes a calculated answer requires more significant digits. Here one or more zeroes are added. 4.0 x 1.0 = 4 needs to be reported as 4.0

12. Mathematical operations & Significant Figures When multiplying or dividing use fewest significant figures  The same number of significant figures as the measurement with the fewest significant figures. 5 Example: 110.5 8 x 0.048 8840 0 4420 0 0000 3040 005.3040 When adding or subtracting use fewest decimal places  The same number of decimal places as the measurement with the fewest decimal places. 4 4 2. 5 4 two decimal places 3 - 3 6. 3 one decimal place 2 42 6. 2 46. 2 answer with one decimal place 12 3 110.5 x 0.048 = 5.304 = 5. 3 (rounded) 4 SF 2 SF calculator 2 SF

13. Not every number is a measured number, non-measured numbers are said to be exact.  When objects are counted. Counting objects 2 soccer balls 4 pizzas  From numbers in a defined relationship. Defined relationships 1 foot = 12 inches 1 meter = 100 cm  From integer values in equations. In the equation for the radius of a circle, the 2 is exact. radius of a circle = diameter of a circle 2 13 Exact Numbers

14. Units of Measurement metric system The units used in most of the world, and everywhere by scientists, are those found in the metric system (~ 1790). International System SI In an effort to improve the uniformity of units used in the sciences, the metric system was modified and called the International System of Units (Système International) or SI (~ 1960). MeasurementMetricSI Lengthmeter (m)meter (m) Volumeliter (L)cubic meter (m 3 ) Massgram (g)kilogram (kg) Timesecond (s)second (s) TemperatureCelsius (  C)Kelvin (K) 14 The metric system or SI (international system) is a decimal system based on 10. A unit can be increased or decrease by a factor of 10 Unit x 10  increases its value 1 x 10= 10 = 1x10 1 1 x 10 x 10= 100 = 1x10 2 1 x 10 x 10 x 10= 1000 = 1x10 3 Unit ÷ 10  decreases its value 1/10 = 0.10 = 1x10 -1 1/10x10= 0.010 = 1x10 -2 1/10x10x10= 0.001 = 1x10 -3 kilo deci centi milli

15. 15

16. equality An equality states the same magnitude of measurement in two different units. 16 same system use exact numbers  The numbers in an equality of the same system are definitions and use exact numbers. not 1 m = 1000 mm both 1 and 1000 are exact and not used to determine significant figures.  Different systems count as significant figures  Different systems (metric and U.S.) use measured numbers and count as significant figures. 1 lb. = 454 g Here, 454 has 3 sig. figs. and the 1 is considered to be exact.

17.  It is a ratio obtained from an equality.Equality: 1 in. = 2.54 cm  It can be inverted to give a second conversion factors.1 in. and 2.54 cm 2.54 cm 1 in. May be obtained from information in a word problem. The cost of one gallon (1 gal) of gas is $2.54. 1 gallon of gasand $2.54 $2.54 1 gallon of gas Any ratio can be used as a conversion factor. Percent % = part x 100 A food contains 30% fat: whole 30 g fat and 100 g food 100 g food30 g fat Densityd = mass the density of a liquid is 3.8g volumemL Equalities provide conversion factors. 17 1 in. 2.54 cm

18. 18 6. Perform the following calculations of measured numbers. Give the answers with the correct number of significant figures: 7. For each calculation, round the answer to give the correct number of significant figures. a. 235.05 + 19.6 + 2 = 1) 257 2) 256.73) 256.65 b. 58.925 - 18.2 =1) 40.725 2) 40.733) 40.7 8. Write the equality and conversion factors for each of the following: a. jewelry that contains 18% gold b. one gallon of gas is $ 2.95 Practice

19. 19 Problem Solving A person has a height of 180 cm. What is the height in inches? 180 cm x 1 in = 71 in 2.54 cm How many minutes are in 1.4 days? 1.4 days x 24 hr. x 60 min = 2.0 x 10 3 min 1 day 1 hr. givenwant You must read the problem carefully and identify what data is given and what they want you to find. The info is usually a conversion factor. Start solving the problem by the following set-up: given want info conversion factor(s) given x conversion factor(s) = want

20. 20 9. Write a complete set-up and solve: a. If a ski pole is 3.0 feet in length, how long is the ski pole in mm? b. How many lb of sugar are in 120 g of candy if the candy is 25% (by mass) sugar? c. An antibiotic dosage of 500 mg is ordered. If the antibiotic is supplied in liquid form as 250 mg in 5.0 mL, how many mL would be given? d. Synthroid is used as a replacement or supplemental therapy for diminished thyroid function. A dosage of 0.200 mg is prescribed with tablets that contain 50 µg of Synthroid. How many tablets are required to provide the prescribed medication? Practice