1 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 every measurement has a number and a unit 4.5 g kg 25.0 ºC lb. CHEMISTRY significant figures it is a statement of accuracy: (very accurate = very close to the real value) Here we use significant figures meters number + unit scientific notation it is a statement of magnitude: (very small, small, large, very large) Here we use scientific notation

2 scientific notation A number in scientific notation contains a coefficient and a power of x x 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 are shown as a power of ten. 4 Positive if moved to the left = 5.2 x spaces left -3 Negative if moved to the right = 3.78 x spaces right

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

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 ± 0.1{ 4.6, 4.7, 4.8 }

5 1. Find the smallest graduation: Subtract the values of any two adjacent labeled graduations and divide by the number of intervals between them. 2. Take the uncertainty to be 10% of the smallest graduation: Follow the steps and determine the length.

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 has 3 significant numbers 6 Summary

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.

Rules to determine significant figures

Practice 4. State the number of significant figures in each of the following measurements: a mb Lc gd m 5. Which answer(s) contains 3 significant figures? a) b) c) 4.76 x 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 x 10 –3 2. Write the following as standard numbers: a.7.2 x 10 –3 m b. 2.4 x 10 5 g 1. Write the following measurements in scientific notation: a L b m 6. All the zeros are significant in 1) ) ) x The number of significant figures in 5.80 x 10 2 is 1) one2) two3) three

8. Follow the steps and obtain a measurement for the solids and liquid. Practice (d)

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 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 to 3 significant figures drop the digits 32 = or greater If the first digit to be dropped is 5 or greater, the last retained digit is increased by 1. To round to 2 significant figures drop 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 reported as 4.0

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.  Rounding to obtain the correct number of significant figures. Example: x = = 5.3 (rounded) 4 SF 2 SF calculator 2 SF When adding or subtracting use fewest decimal places  The same number of decimal places as the measurement with the fewest decimal places.  Rounding rules to adjust the number of digits in the answer two decimal place __ one decimal places answer with one decimal place 12

Exact Numbers 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

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 = 1x x 10 x 10= 100 = 1x x 10 x 10 x 10= 1000 = 1x10 3 Unit ÷ 10  decreases its value 1/10 = 0.10 = 1x /10x10= = 1x /10x10x10= = 1x10 -3 kilo deci centi milli

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equality An equality states the same 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 exact.

 It is a ratio obtained from an equality (see p. 33 table 1.9).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 $ gallon of gasand $2.94 $ gallon of gas Any ratio can be used as a conversion factor. Percent % = part x 100 whole A food contains 30% fat:30 g fat and 100 g food 100 g food30 g fat Densityd = mass volume the density of a liquid is 3.8g mL Equalities provide conversion factors. 17

18 9. Perform the following calculations of measured numbers. Give the answers with the correct number of significant figures: 10. For each calculation, round the answer to give the correct number of significant figures. a = 1) 257 2) ) b =1) ) ) Write the equality and conversion factors for each of the following: a. meters and centimetersb. jewelry that contains 18% gold c. one gallon of gas is $ 2.95 d. hours and minutese. Density of water is 1.00 g/mL

19 Problem Solving Conversion factors Use Conversion factors to solve problems: givewant In general, problems  give you something and want you to find something else conversion factor(s) given x conversion factor(s) = want 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.

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. If olive oil has a density of 0.92 g/mL, how many liters of olive oil are in 285 g of olive oil? c. How many lb of sugar are in 120 g of candy if the candy is 25% (by mass) sugar? d. 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? e. Synthroid is used as a replacement or supplemental therapy for diminished thyroid function. A dosage of mg is prescribed with tablets that contain 50 µg of Synthroid. How many tablets are required to provide the prescribed medication? Practice