CHAPTER 2 MEASUREMENT AND PROBLEM SOLVING Problems 1 64 69 88 91 120 123 124 2 1 Measuring Global Temperatures measurement a number with attached units When scientists collect data it is important that they record the measurements as accurately as possible and the measurements must reflect the accuracy and precision of the instruments used to collect that data Consider the following plot of global land ocean temperatures based on measurements taken from meteorological stations and ship and satellite temperature SST measurements Source Hansen J Mki Sato R Ruedy K Lo D W Lea and M Medina Elizade 2006 Global temperature change Proc Natl Acad Sci 103 14288 14293 doi 10 1073 pnas 0606291103 http pubs giss nasa gov abstracts 2006 Hansen etal 1 html The plot above shows annual mean average temperatures in black 5 year mean temperatures in red and the uncertainty as green bars Ex 1 Based on this plot how have global land ocean temperatures changed since the 1950s CHEM 121 Chapter 2 v0912 page 1 of 17 2 3 SIGNIFICANT FIGURES or SIG FIGS Writing Numbers to Reflect Precision To measure one uses instruments tools such as a ruler balance etc All instruments have one thing in common UNCERTAINTY INSTRUMENTS CAN NEVER GIVE EXACT MEASUREMENTS When a measurement is recorded all the given numbers are known with certainty given the markings on the instrument except the last number is estimated The digits are significant because removing them changes the measurement s uncertainty Thus when measurements are recorded they are recorded to one more decimal place than the markings for analog instruments they are recorded exactly as displayed on electronic digital instruments LENGTH generally reported in meters centimeters millimeters kilometers inches feet miles Know the following English English conversions 1 foot 12 inches 1 yard 3 feet Example Using Rulers A B and C below indicate the measurement to the line indicated for each ruler Assume these are centimeter rulers so show the each measurement has units of cm Circle the estimated digit for each measurement Ruler A 0 1 2 3 4 5 0 1 2 3 4 5 Ruler B Ruler C 4 1 A 4 2 4 3 4 4 B C Measurement Increment of the smallest markings on ruler of sig figs Thus a measurement is always recorded with one more digit than the smallest markings on the instrument used and measurements with more sig figs are usually more accurate CHEM 121 Chapter 2 v0912 page 2 of 17 Guidelines for Sig Figs if measurement is given Count the number of digits in a measurement from left to right 1 When there is a decimal point For measurements greater than 1 count all the digits even zeros 62 4 cm has 3 sig figs 5 0 m has 2 sig figs 186 100 g has 6 s f For measurements less than 1 start with the first nonzero digit and count all digits even zeros after it 0 011 mL and 0 00022 kg each have 2 sig figs 2 When there is no decimal point Count all non zero digits and zeros between non zero digits e g 125 g has 3 sig figs 1007 mL has 4 sig figs Placeholder zeros may or may not be significant e g 1000 may have 1 2 3 or 4 sig figs Example Indicate the number of significant digits for the following a 165 3 g c 90 40 m e 0 19600 g b 105 cm d 100 00 L f 0 0050 cm 2 5 THE BASIC UNITS OF MEASUREMENT VOLUME Amount of space occupied by a solid gas or liquid generally in units of liters L milliliters mL or cubic centimeters cm3 Know the following 1 L 1 dm3 1 mL 1 cm3 These are both exact Note When the relationship between two units or items is exact we use the to mean equals exactly rather than the traditional sign also know the following equivalents in the English system 1 gallon 4 quarts MASS 1 quart 2 pints 1 pint 2 cups a measure of the amount of matter an object possesses measured with a balance and NOT AFFECTED by gravity usually reported in grams or kilograms WEIGHT a measure of the force of gravity usually reported in pounds abbreviated lbs mass weight mass acceleration due to gravity CHEM 121 Chapter 2 v0912 page 3 of 17 Mass is not affected by gravity 2 2 SCIENTIFIC NOTATION Some numbers are very large or very small difficult to express Avogadro s number 602 000 000 000 000 000 000 000 an electron s mass 0 000 000 000 000 000 000 000 000 000 91 kg To handle such numbers we use a system called scientific notation Regardless of their magnitude all numbers can be expressed in the form N 10n where N digit term a number between 1 and 10 so there can only be one number to the left of the decimal point n an exponent a positive or a negative integer whole To express a number in scientific notation Count the number of places you must move the decimal point to get N between 1 and 10 Moving decimal point to the right if 1 negative exponent Moving decimal point to the left if 1 positive exponent Example Express the following numbers in scientific notation to 3 sig figs 555 000 0 000888 602 000 000 000 000 000 000 000 CHEM 121 Chapter 2 v0912 page 4 of 17 Some measurements may be rounded to a number of sig figs requiring scientific notation For example Express 100 0 g to 3 sig figs Express 100 0 g to 2 sig figs Express 100 0 g to 1 sig fig UNBIASED ROUNDING or ROUND TO EVEN METHOD How do we eliminate nonsignificant digits If first nonsignificant digit 5 just drop the nonsignificant digits If first nonsignificant digit 5 raise the last sig digit by 1 and drop nonsignificant digits to 3 s f e g 3 14501 3 15 since the nonsig figs are 501 in 3 14501 Express each of the following with the number of sig figs indicated to 3 sig figs a 648 75 b 23 6500 c 64 55 d 0 00123456 e 1 234 567 f 1975 to 3 sig figs to 3 sig figs to 3 sig figs to 5 sig figs to 2 sig figs When necessary express measurements in scientific notation to clarify the number of sig figs 2 4 SIGNIFICANT FIGURES IN CALCULATIONS ADDING SUBTRACTING MEASUREMENTS When adding and subtracting measurements your final value is limited by the measurement with the largest uncertainty i e the measurement with the fewest decimal places MULTIPLYING DIVIDING MEASUREMENTS When multiplying or dividing measurements the final value is limited by the measurement with the least number of significant figures CHEM 121 Chapter 2 v0912 page 5 of 17 Ex 1 7 4333 g 8 25 g 10 781 g Ex 2 13 50 cm 7 95 cm 4 00 cm Ex 3 9 75 mL 7 35 mL Ex 4 101 755 g 25 75 cm 10 25 cm 8 50 cm MULTIPLYING …