Metric Prefixes UNITS & MEASUREMENT 10/6/2015 WHY DO UNITS AND MEASUREMENT MATTER?

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1 UNITS & MEASUREMENT WHY DO UNITS AND MEASUREMENT MATTER? Chemistry In Action On 9/3/99, $15,000,000 Mars Climate Orbiter entered Mar s atmosphere 100 km (6 miles) lower than planned and was destroyed by heat. Problem: Two different groups of engineers used different (metric vs english) systems of units to measure thrust. And didn t tell each other. 1 lb = 1 N 1 lb = 4.45 N International System of Units (SI) Metric Prefixes Powers of 10 1

2 Volume SI derived unit for volume is cubic meter (m 3 ) 1 cm 3 = (1 x 10 - m) 3 = 1 x 10-6 m 3 1 dm 3 = (1 x 10-1 m) 3 = 1 x 10-3 m 3 1 L = 1000 ml = 1000 cm 3 = 1 dm 3 1 ml = 1 cm 3 QUESTION: At 4 degrees Celsius, what does one ml (or one cm 3 ) of pure water weigh? Scientific Notation The number of atoms in 1 g of carbon: 60,00,000,000,000,000,000, x 10 3 The mass of a single carbon atom in grams: N is a number between 1 and x 10-3 N x 10 n n is a positive or negative integer Scientific Notation move decimal left move decimal right n > 0 n < = x = 7.7 x 10-6 Addition or Subtraction 1. Write each quantity with the same exponent n. Combine N 1 and N 3. The exponent, n, remains the same 4.31 x x 10 3 = 4.31 x x 10 4 = 4.70 x 10 4 Scientific Notation Multiplication 1. Multiply N 1 and N (4.0 x 10-5 ) x (7.0 x 103 ) = (4.0 x 7.0) x (10. Add exponents n 1 and n -5+3 ) = 8 x 10 - =.8 x 10-1 Division 1. Divide N 1 and N 8.5 x x 10 9 =. Subtract exponents n 1 and n ( ) x = x 10-5 Sources of Error Precision and Accuracy Why we need to worry about SIGNIFICANT FIGURES! All measurement inherently contains error. No instrument is perfect, nor is any instrument reader!

3 Scientists are concerned with two aspects of instrument error First, how close is the measured value to the true value? Secondly, how reproducible is the measurement? The scale below has not been zeroed, so the weight it measures will be inaccurate. ACCURACY PRECISION Even if the scale is very precise, and it measures very close to the same reading every time, the weight it measures will still be off. Of course, the scale might be very out of whack and read differently every time, resulting in... POOR ACCURACY, POOR PRECISION Of course, the goal of all measurement is to hit the bull s eye! Which section in the graph below represents good precision and good accuracy? (Assume that the true value lies on or near the dotted line at 5.0 grams). GOOD ACCURACY, GOOD PRECISION 3

4 Uncertainty in Measurement Precision is always limited by the scale of the instrumentthe more finely divided the scale, the more precise and accurate the instrument. Estimate the length of this wood block (assume the units are cm.) 60.7 cm We have to guess this last one ALWAYS GUESS ONE NUMBER BETWEEN THE LINES Let s look at the volume in this graduated cylinder Make an estimate of the volume: uncertain 31.5 ml digit: must read between the lines certain digits: can be read right off the scale For example, what is the density of the rock of granite shown below if its mass is grams and its volume is 58.7 cm 3? Hey! Wait a minute! Can we really be sure of this value out to 7 decimal places? d = m/v = g 58.7 cm 3 = g/cm 3 Significant Figures The rule of thumb when reporting measurements is to report all certain digits plus the first uncertain digit. The numbers recorded in a measurement are called significant figures. Now try to read this cylinder to the correct number of significant figures. 4

5 Here s a second accepted practice for reporting measurements correctly: You should not report any more sig figs in a calculated value than were in the basic measurements to begin with. RULES FOR DETERMINING THE NUMBER OF SIGNIFICANT FIGURES IN A NUMBER 1. IF IT ISN T A ZERO, IT IS SIGNIFICANT! And you have to count it: 3.4 has 3 significant figures has 4 significant figures How many does 4.3 have? RULES FOR DETERMINING THE NUMBER OF SIGNIFICANT FIGURES IN A NUMBER (continued) Another way to keep things straight: Atlantic and Pacific method. ZEROS ARE TRICKY and there are 3 kinds of zeros: a. Leading Zeros: NEVER COUNT! sig figs sig figs How many does 0.45 have? b. Sandwiched Zeros: ALWAYS COUNT! sig figs sig figs How many does have? c. Trailing Zeros: COUNT ONLY IF THERE IS A DECIMAL! sig figs sig fig How many does have? Pacific Ocean Atlantic Ocean Atlantic: decimal is absent. Approach the number from the Atlantic Ocean side (from the right) and count all digits as significant after you hit shore (hit the first non zero number) 69,000 Decimal absent. Two significant figures. Pacific: decimal is present. Approach the number from the Pacific Ocean side (from the left) and count all digits as significant after you hit shore (hit the first non zero number) 5

6 Decimal present. Two significant figures Significant Figures Review Any digit that is not zero is significant 1.34 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.0 mg 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 How many significant figures are in each of the following measurements? 4 ml significant figures 3001 g 4 significant figures m 3 3 significant figures 6.4 x 10 4 molecules significant figures 560 kg significant figures 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 one significant figure after decimal point two significant figures after decimal point round off to 0.79 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 figs round to 3 sig figs = sig figs = round to sig figs BEWARE OF EXACT NUMBERS! An exact number is a number that is counted or defined. For instance, there are 100 cm in 1 meter. Or, there are 4 people in the room. These are exact numbers, not measurements. Therefore, these would not limit the number of significant figures in any value calculated from them. 6

7 Exact Numbers Significant Figures 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? = = 6.67 = 7 3 Because 3 is an exact number Round up on rounding! 5 s and higher, round up, 4s and lower round down. Make sure you leave your answer to the correct number of significant figures! Round to the fewest Addition & Subtraction = decimal places Multiplication & Division = Round to the fewest significant figures Dimensional Analysis Method of Solving Problems 1. Determine which unit conversion factor(s) are needed. Carry units through calculation 3. If all units cancel except for the desired unit(s), then the problem was solved correctly. given quantity x conversion factor = desired quantity The speed of sound in air is about 343 m/s. What is this speed in miles per hour? conversion units needed: meters to miles seconds to hours 1 mi = 1609 m 1 min = 60 s 1 hour = 60 min given unit x desired unit given unit = desired unit 343 m s x 1 mi x 60 s 1609 m 1 min x 60 min = 767 mi 1 hour hour K = 0 C K = 0 0 C 373 K = C 0 F = 9 x 0 C F = 0 0 C 1 0 F = C 7