Matter measurement and problem solving

measurement and problem solving chemistry and measurement problem solving examples
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Dr.SamuelHunt,United Arab Emirates,Teacher
Published Date:21-07-2017
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Measurement and Problem Solving www.ThesisScientist.comWhat Is a Measurement? • Quantitative = quantity and it must have a unit • Comparison to an agreed upon standard. • accuracy www.ThesisScientist.comScientists have measured the average global temperature rise over the past century to be 0.6 °C • Quantity is 0.6 the unit is°C • Comparison to an agreed upon standard is Celsius temperature scale. • Accuracy: The confidence in the measurement is determined by looking at th’s the last digit, here it is in the 1/10 position, so the certain is plus and minus 1/10 or between 0.5 and 0.7 °C. www.ThesisScientist.comScientific Notation A way of writing large and small numbers. www.ThesisScientist.comBig and Small Numbers • We commonly measure The sun’s objects that are many times diameter is larger or smaller than our 1,392,000,000 m. standard of comparison. • Writing large numbers of zeros is tricky and confusing. An atom’s Not to mention there’s the 8- average diameter is digit limit of your calculator 0.000 000 000 3 m. www.ThesisScientist.comExponents • When the exponent on 10 is positive, it means the number is that many powers of 10 larger. 9 Sun’s diameter = 1.392 x 10 m = 1,392,000,000 m. • When the exponent on 10 is negative, it means the number is that many powers of 10 smaller. -10 Average atom’s diameter = 3 x 10 m = 0.0000000003m www.ThesisScientist.comScientific Notation • To compare numbers written in scientific notation: First compare exponents on 10. If exponents are equal, then compare decimal numbers Exponent 5 2 1.23 x 10 4.56 x 10 -8 -2 -5 1.23 x 10 4.56 x 10 7.89 x 10 10 10 7.89 x 10 1.23 x 10 Decimal part Exponent part www.ThesisScientist.comWriting a Number in Scientific Notation, Continued 12340 1. Locate the decimal point. 12340. 2. Move the decimal point to obtain a number between 1 and 10. 1.234 n 3. Multiply the new number by 10 .  Where n is the number of places you moved the decimal point. 4 1.234 x 10 4. If you moved the decimal point to the left, then n is +; if you moved it to the right, then n is − . 4 1.234 x 10 www.ThesisScientist.comWriting a Number in Scientific Notation, Continued 0.00012340 1. Locate the decimal point. 0.00012340 2. Move the decimal point to obtain a number between 1 and 10. 1.2340 n 3. Multiply the new number by 10 .  Where n is the number of places you moved the decimal point. 4 1.2340 x 10 4. If you moved the decimal point to the left, then n is +; if you moved it to the right, then n is − . -4 1.2340 x 10 www.ThesisScientist.comWriting a Number in Standard Form -6 1.234 x 10 • Since exponent is -6, make the number smaller by moving the decimal point to the left 6 places. When you run out of digits to move around, add zeros. Add a zero in front of the decimal point for decimal numbers. 000 001.234 0.000 001 234 www.ThesisScientist.comPractice—Write the Following in Scientific Notation, Continued 2 0 123.4 = 1.234 x 10 8.0012 = 8.0012 x 10 5 -3 145000 = 1.45 x 10 0.00234 = 2.34 x 10 1 -2 25.25 = 2.525 x 10 0.0123 = 1.23 x 10 0 -6 1.45 = 1.45 x 10 0.000 008706 = 8.706 x 10 www.ThesisScientist.comPractice—Write the Following in Standard Form, Continued 3 0 2.1 x 10 = 2100 4.02 x 10 = 4.02 -4 1 9.66 x 10 = 0.000966 3.3 x 10 = 33 -2 0 6.04 x 10 = 0.0604 1.2 x 10 = 1.2 www.ThesisScientist.comNumbers 1. Exact 2. Measured: Significant Figures www.ThesisScientist.comExact Numbers vs. Measurements • Exact: Sometimes you can determine an exact value for a quality of an object. A. Often by counting. • Pennies in a pile. B. Sometimes by definition th • 1 ounce is exactly 1/16 of 1 pound. • Measured: Whenever you use an instrument to compare a quality of an object to a standard, there is uncertainty in the comparison. www.ThesisScientist.comExact Numbers • Exact numbers have an unlimited number of significant figures. • A number whose value is known with complete certainty is exact. From counting individual objects. From definitions. • 1 cm is exactly equal to 0.01 m. • 20 .05 = 1.0000000000000 • 12 inches = 1.000000000000000000000000 ft www.ThesisScientist.com4 fundamental measuring instruments 1. Length 2. Mass 3. Time 4. Temperature www.ThesisScientist.comHow do we make a Measurement • Measurements are written to indicate the uncertainty in the measurement. • The system of writing measurements we use is called significant figures. • When writing measurements, all the digits written are known with certainty except the last one, which is an estimate. 4 45 5.87 .872 2 Estimated Certain www.ThesisScientist.comReading a Measuring Instrument/Device For any Digital Device record ALL the digits www.ThesisScientist.comReading a Measuring Instrument/Device 1. Record all the numbers you can see 2. Make ONE Guess www.ThesisScientist.comSkillbuilder 2.3—Reporting the Right Number of Digits • A thermometer used to measure the temperature of a backyard hot tub is shown to the right. What is the temperature reading to the correct number of digits? www.ThesisScientist.com