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# Measurements and alculations

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### Measurements and alculations

1. 1. • Is used to represent very small and very large numbers easily so that they are easy to write and read with less errors• Large numbers are represented by a positive exponent of ten • 9.8 x 1012 = 9,800,000,000,000• Small numbers are represented by a negative exponent of ten • 9.8 x 10-12 = 0.0000000000098• See textbook review/rules list p. 127
2. 2. • A measurement always consists of two parts: a number and a unit• The unit tells the reader what scale/standard was used and makes the number meaningful• Scientists use the SI (System Internationale in French) system of units based upon the metric system Measurement Unit Instrument Length Meter Meter stick Mass Gram Balance Volume Liter Graduated cylinder
3. 3. • Every measurement has some degree of uncertainty • This is dependent upon the instrument used for measuring• All numbers recorded in a measurement = the significant figures of that measurement • They include all certain numbers plus the first uncertain number • Ex: if the uncertainty for a measurement of 1.86 is +/- .01, then the measurement could actually be: 1.86, 1.85, or 1.87
4. 4. 1. All nonzero numbers are significant2. Zeros are sometimes significant a) Leading zeros are never significant (.0025 has only 2 sig figs) b) Captive zeros are always significant (.2005 has 4 sig figs) c) Trailing zeros are sometimes significant  Only if there is a decimal point in the number  No decimal point means those zeros are not significant  Ex: 20 has one sig fig, 20. has two sig figs , 20.0 has three sig figs  The number of sig figs in the examples above alert the reader as to the type of measurement device used
5. 5. • Your final answer can never have more sig figs than the least precise measurement.• Rounding off your answer can accomplish this • If the number to be removed is less than five, the preceding digit remains the same • If the number to be removed is/is greater than five, the preceding digit is increased by one • If you are doing a series of calculations, round at the last step only, not at each separate intermediary step
6. 6. • For multiplication and • For addition and division, your answer subtraction, your should contain the # answer should contain of sig figs equal to the the # of decimal least # of sig figs in places equal to the your problem least # of decimal places in your • 4.56 x 1.4 = 6.384 problem • Round to 2 sig figs: 6.4 • 12.11 + 18.0=30.11 • Round to 1 dec place: 30.1
7. 7. • Dimensional analysis (DA) is the process we use to solve many chemistry problems we will do throughout the year in our chemistry class (known as stoichiometry) • DA uses conversion factors and canceling out methodology to derive the correct answer and unit• We will practice it using metric conversion because they are familiar to you • If you simply solve the metric conversion using shortcuts you have used in the past, you are missing the opportunity to practice the DA technique you will need when we tackle these more challenging scenarios later in the semester• Keep at it! DA takes time and practice. You will get it if you are persistent and engaged as we work through our practice exercises available on School Loop. 