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## Chemistry 1 – McGill Chapter 3 Scientific Measurement

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**Chemistry 1 – McGillChapter 3Scientific Measurement**WARNING: Learn it now...it will be used all year in Chemistry!!!**3.1**Qualitative measurements • measurements that give results in a descriptive, non-numerical form. Examples: He is tall Electrons are tiny**Quantitative measurements**• measurement that gives results in a definite form, usually as numbers and units. Examples: He is 2.2 m tall Electrons are 1/1840 times the mass of a proton**What is Scientific Notation?**• Scientific notation is a way of expressing really big numbers or really small numbers. • It is most often used in “scientific” calculations where the analysis must be very precise. • For very large and very small numbers, scientific notation is more concise.**Scientific notation consists of two parts:**• A number between 1 and 10 • A power of 10 N x 10x**To change standard form to scientific notation…**• Place the decimal point so that there is one non-zero digit to the left of the decimal point. • Count the number of decimal places the decimal point has “moved” from the original number. This will be the exponent on the 10. • If the original number was less than 1, then the exponent is negative. If the original number was greater than 1, then the exponent is positive.**Scientific Notation**• a number is written as the product of two numbers: a coefficient and 10 raised to a power. Examples: 567000 = 5.67 X 105 0.00231 = 2.31 X 10-3**Examples:**Convert to or from Scientific Notation: 2.41 x 102 6.015 x 103 1.62 x 10-2 5.12 x 10-1 662 .0034 241 = 6015 = .0162 = .512 = 6.62 x 102 = 3.4 x 10-3 =**Learning Check**• Express these numbers in Scientific Notation: • 405789 • 0.003872 • 3000000000 • 2 • 0.478260 4.05789 X 105 3.872 X 10-3 3 X 109 2 X 100 4.78260 X 10-1**FYI: “EE” button on calc= typing “X10^”**Scientific Notation Cont. (This is important to master!!!) 6.25 x 103 - 2.01 x 102 = (2.15 x 103)(6.1 x 105)(5.0 x 10-6) = 3.25 x 108 = 3.6 x 107 6.05 x 103 6.6 x 103 9.03**Accuracy Vs. Precision**What do you think the differences are? Ideas anyone???**3.2**Accuracy • the measure of how close a measurement comes to the actual or true value of whatever is measured. • how close a measured value is to the accepted value. Precision • the measure of how close a series of measurements are to one another.**Can you hit the bull's-eye?**Three targets with three arrows each to shoot. How do they compare? Both accurate and precise Precise but not accurate Neither accurate nor precise Can you define accuracy and precision?**Accurate?**No Precise? Yes 10**Precise?**Yes Accurate? Yes 12**Accurate?**Maybe? Precise? No 13**Precise?**We cant say! Accurate? Yes 18**In terms of measurement**• Three students measure the room to be 10.2 m, 10.3 m and 10.4 m across. • Were they precise? • Were they accurate?**Percent Error Formula:**% Error = accepted value- experimental value x 100 accepted value *always a positive number- indicated by the absolute value sign* You will use this formula when checking the accuracy of your experiment.**think about a**TARGET**Significant Figures – includes all of the digits that are**known plus a last digit that is estimated. ! FYI: These rules are not fun, but they will save you many points in the future if you learn them NOW!**Rules for determining Significant Figures1. All non-zero**digits are significant. 1, 2, 3, 4, 5, 6, 7, 8, 9**2. Zeros between non-zero digits are significant. (AKA**captive zeros) 102 7002**3. Leading zeros (zeros at the beginning of a measurement)**are NEVER significant. 00542 0.0152**4. Trailing zeros (zeros after last integer) are**significant only if the number contains a decimal point. 210.0 0.860 210**5. All digits are significant in scientific notation.**2.1 x 10-5 6.02 x 1023 Time to practice!!**Exact numbers have unlimited Significant Figures**Do not use these when you are figuring out sig figs… Examples: 1 dozen = exactly 12 29 people in this room**Examples:How many significant digits do each of the**following numbers contain: a) 1.2 d) 4600b) 2.0 e) 23.450c) 3.002 f) 6.02 x 1023 2 2 2 5 3 4**Learning Check**A. Which answers contain 3 significant figures? • 0.4760 2) 0.00476 3) 4760 B. All the zeros are significant in 1) 0.00307 2) 25.300 3) 2.050 x 103 C. 534,675 rounded to 3 significant figures is 1) 535 2) 535,000 3) 5.35 x 105**Solution**A. Which answers contain 3 significant figures? 1) 0.47602) 0.00476 3) 4760 B. All the zeros are significant in 1) 0.003072) 25.300 3) 2.050 x 103 C. 534,675 rounded to 3 significant figures is 1) 5352) 535,000 3) 5.35 x 105**Learning Check**In which set(s) do both numbers contain the samenumber of significant figures? 1) 22.0 and 22.00 2) 400.0 and 40 3) 0.000015 and 150,000**Solution**In which set(s) do both numbers contain the samenumber of significant figures? 3) 0.000015 and 150,000**Learning Check**State the number of significant figures in each of the following: A. 0.030 m 1 2 3 B. 4.050 L 2 3 4 C. 0.0008 g 1 2 4 D. 3.00 m 1 2 3 E. 2,080,000 bees 3 5 7**Learning Check**State the number of significant figures in each of the following: A. 0.030 m 1 2 3 B. 4.050 L 2 3 4 C. 0.0008 g 1 2 4 D. 3.00 m 1 2 3 E. 2,080,000 bees 3 5 7**Rounding Rules:** 5 round up < 5 round down (don’t change) Examples: Round 42.63 to 1 significant digit = Round 61.57 to 3 sig. digs.= Round 0.01621 to 2 = Round 65,002 to 2 sig. digs. = 40 61.6 0.016 65,000**Addition and Subtraction**The measurement with the fewest significant figures to the right of the decimal point determines the number of significant figures in the answer.**Examples:**Solve using correct significant figures 45.756 m + 62.1 m = 75.263 m + 1123.93 m = 107.9 1199.19**Multiplying and Dividing Measurements**The measurement with the fewest significant figures determines the number of significant figures in the answer.**Examples:Solve using correct significant figures:**3.43 m X 6.4253 m = 45.756 m X 1.2 m = 45.01 m / 2.2 m = 22.0 m2 55 m2 20. ***Why did the “m” unit go away on the last example?*** Noticethe decimal!**Uncertainty**In lab, you record all numbers you know for sure plus the first uncertain digit. The last digit is estimated and is said to be uncertain but still considered significant. • Graduated cylinders have markings to the nearest mL (milliliter) and you will determine volume to the nearest 0.1 mL… because that is ONE DIGIT OF UNCERTAINTY.**International System of Units**• revised version of the metric system • abbreviated SI All units, their meanings and values can be found on pgs. 63,64,65. Meter (m) – Liter (L) – Gram (g) – SI unit for length SI unit for volume SI unit for mass**Some Tools for Measurement**Which tool(s) would you use to measure: A. temperature B. volume C. time D. weight**Solution**A. temperature thermometer B.volume measuring cup, graduated cylinder C.time watch D. weightscale**Learning Check**Match L) length M) mass V) volume ____ A. A bag of tomatoes is 4.6 kg. ____ B. A person is 2.0 m tall. ____ C. A medication contains 0.50 g Aspirin. ____ D. A bottle contains 1.5 L of water. M L M V**Learning Check**What are some U.S. units that are used to measure each of the following? A. length B. volume C. weight D. temperature**Solution**Some possible answers are A.length inch, foot, yard, mile B. volume cup, teaspoon, gallon, pint, quart C. weight ounce, pound (lb), ton D. temperature °F**Metric Prefixes**• Kilo- means 1000 of that unit • 1 kilometer (km) = 1000 meters (m) • Centi- means 1/100 of that unit • 1 meter (m) = 100 centimeters (cm) • 1 dollar = 100 cents • Milli- means 1/1000 of that unit • 1 Liter (L) = 1000 milliliters (mL)