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## Standards for Measurement

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**Mass : The quantity or amount of matter that an object**possesses. • Fixed • Independent of the object’s location • Weight: A measure of the earth’s gravitational attraction for an object. • Not fixed • Depends on the object’s location. • Matter: Anything that has mass and occupies space.**Measurements**• Experiments are performed. • Numerical values or data are obtained from these measurements.**numerical value**70 kilograms = 154 pounds unit Form of a Measurement**known**estimated Significant Figures • The number of digits that are known plus one estimated digit are considered significant in a measured quantity 5.16143**known**estimated Significant Figures • The number of digits that are known plus one estimated digit are considered significant in a measured quantity 6.06320**The temperature 21.2oC is expressed to 3 significant**figures. Temperature is estimated to be 21.2oC. The last 2 is uncertain.**The temperature 22.0oC is expressed to 3 significant**figures. Temperature is estimated to be 22.0oC. The last 0 is uncertain.**Significant Figures**All nonzero numbers are significant. 461**Significant Figures**All nonzero numbers are significant. 461**Significant Figures**All nonzero numbers are significant. 461**Significant Figures**All nonzero numbers are significant. 3 Significant Figures 461**Significant Figures**A zero is significant when it is between nonzero digits. 3 Significant Figures 401**Significant Figures**A zero is significant when it is between nonzero digits. 5 Significant Figures 9 3 . 0 0 6**Significant Figures**A zero is significant when it is between nonzero digits. 3 Significant Figures 9 . 0 3**Significant Figures**A zero is significant at the end of a number that includes a decimal point. 5 Significant Figures 5 5 . 0 0 0**Significant Figures**A zero is significant at the end of a number that includes a decimal point. 5 Significant Figures 2 . 1 9 3 0**Significant Figures**A zero is not significant when it is before the first nonzero digit. 1 Significant Figure 0 . 0 0 6**Significant Figures**A zero is not significant when it is before the first nonzero digit. 3 Significant Figures 0 . 7 0 9**Significant Figures**A zero is not significant when it is at the end of a number without a decimal point. 1 Significant Figure 5 0 0 0 0**Significant Figures**A zero is not significant when it is at the end of a number without a decimal point. 4 Significant Figures 6 8 7 1 0**Very large and very small numbers are often encountered in**science. 602200000000000000000000 0.00000000000000000000625 • Very large and very small numbers like these are awkward and difficult to work with.**6.25 x 10-21**A method for representing these numbers in a simpler form is scientific notation. 6.022 x 1023 602200000000000000000000 0.00000000000000000000625**Scientific Notation**• Write a number as a power of 10 • Move the decimal point in the original number so that it is located after the first nonzero digit. • Follow the new number by a multiplication sign and 10 with an exponent (power). • The exponent is equal to the number of places that the decimal point was shifted.**Write 6419 in scientific notation.**decimal after first nonzero digit power of 10 6.419 x 103 64.19x102 641.9x101 6419. 6419**Write 0.000654 in scientific notation.**decimal after first nonzero digit power of 10 6.54 x 10-4 0.000654 0.00654 x 10-1 0.0654 x 10-2 0.654 x 10-3**The metric or International System (SI, Systeme**International) is a decimal system of units. • It is built around standard units. • It uses prefixes representing powers of 10 to express quantities that are larger or smaller than the standard units.**International System’s Standard Units of Measurement**Length meter m Quantity Name of Unit Abbreviation Mass kilogram kg Temperature Kelvin K Time second s Amount of substance mole mol Electric Current ampere A Luminous Intensity candela cd**Power of 10**Prefix Symbol Numerical Value Equivalent Prefixes and Numerical Values for SI Units exa E 1,000,000,000,000,000,000 1018 peta P 1,000,000,000,000,000 1015 tera T 1,000,000,000,000 1012 giga G 1,000,000,000 109 mega M 1,000,000 106 kilo k 1,000 103 hecto h 100 102 deca da 10 101 — —1 100**Power of 10**Prefix Symbol Numerical Value Equivalent Prefixes and Numerical Values for SI Units deci d 0.1 10-1 centi c 0.01 10-2 milli m 0.001 10-3 micro 0.000001 10-6 nano n 0.000000001 10-9 pico p 0.000000000001 10-12 femto f 0.00000000000001 10-15 atto a 0.000000000000000001 10-18**Dimensional Analysis**Dimensional analysis converts one unit to another by using conversion factors. unit1 x conversion factor = unit2**Basic Steps**• Read the problem carefully. Determine what is to be solved for and write it down. • Tabulate the data given in the problem. • Label all factors and measurements with the proper units.**Basic Steps**• Determine which principles are involved and which unit relationships are needed to solve the problem. • You may need to refer to tables for needed data. • Set up the problem in a neat, organized and logical fashion. • Make sure unwanted units cancel. • Use sample problems in the text as guides for setting up the problem.**Basic Steps**• Proceed with the necessary mathematical operations. • Make certain that your answer contains the proper number of significant figures. • Check the answer to make sure it is reasonable.**Degree Symbols**degrees Celsius = oC Kelvin (absolute) = K degrees Fahrenheit = oF**To convert between the scales use the following**relationships.**It is not uncommon for temperatures in the Canadian planes**to reach –60oF and below during the winter. What is this temperature in oC and K?**It is not uncommon for temperatures in the Canadian planes**to reach –60oF and below during the winter. What is this temperature in oC and K?**Density is the ratio of the mass of a substance to the**volume occupied by that substance.**The density of gases is expressed in grams per liter.**Mass is usually expressed in grams and volume in ml or cm3.