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**Scientific Measurement**

Chapter 3 Scientific Measurement

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**I. Importance of Measurement A. Quantitative and Qualitative**

1. Qualitative measurement give results in a descriptive, nonnumeric form. 2. Quantitative measurement give results in definite form, usually numbers and units.

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B. Scientific Notation 1. Scientific notation is a number written as the product of two numbers, a coefficient and ten raised to a power. 2. Example = 8.3 x 10-4 3. Scientific notation can be used to express extremely large or small numbers. 4. Multiplication - exponents are added. 5. Division - exponents are subtracted 6. Before you add or subtract numbers in scientific notation, you must make the exponents the same because the exponents determine the location of the decimal point in the original number.

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**II. Uncertainty in Measurements A. Accuracy, Precision, and Error**

1. Accuracy is how close a measurement is to the true value for the quantity. 2. Precision is how close a set of measurements is to one another, regardless of whether the measurements are correct. 3. Measurements have to be accurate and precise, but it is possible to have a source of error repeat in the measurements. 4. Percent error is a way of determining the accuracy of a measurement. 5. The calculation for percent Error is the experimental value subtracted by the literature value divided by the literature value and multiplied by 100. % Error = Experimental value - Literature value x Literature value 6. The literature value is the known value of the measurement.

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**II. Uncertainty in Measurements B. Significant Figure Rules**

1. Numbers other than zero are significant. 2. One or more final zeros used after the decimal point are always significant. (Trailing zeros) 3. Zeros between two other significant figures are always significant. (Captive Zeros) 4. Zeros used solely for the spacing the decimal point are not significant. (Leading Zeros or Place markers)

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**II. Uncertainty in Measurements C. Significant Figures in Calculations**

1. Round to the correct number of significant figures that your answer should have. a. If the digit immediately to the right of the last significant is less than 5, it is dropped. b. If the digit immediately to the right of the last significant is greater than 5, the value of the significant figure is raised by 1. c. If the digit is 5, round to the nearest even number.

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**II. Uncertainty in Measurements C. Significant Figures in Calculations**

2. Addition and subtraction of significant figures must contain the same number of significant figures as the measurement with the least number of significant figures. 3. Multiplication and division of significant figures must contain the same number of significant figures as the measurement with the least number of significant figures.

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**III. Units of Measurements A**

III. Units of Measurements A. SI units (Le Système International d’Unités) 1. The system used in science is the metric system. 2. The units for the measurements. a. Length – meter b. Mass – gram, kilogram, milligram c. Volume – liter, cm3 , ml, µl d. Current – ampere e. Time – seconds f. Pressure – pascal g. Amount of substance – mole h. Temperature – Kelvin or Celsius 1. Celsius = 0°C -100°C 2. Kelvin = °C +273

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**III. Units of Measurements B. Metric Prefixes**

1. The prefixes are placed in front of the unit of measurement. 2. The prefixes for the units. a. Nano– (1/1,000,000,000) = 10-9 b. Micro– (1/1,000,000) = 10-6 c. Milli– (1/1000) = d. Cent– (1/100) e. Deci– (1/10 ) f. Deca– (10 ) g. Hecta– (100) 102 h. Kilo– (1000) 103 3. Weight is the response of mass to gravity. 4. The formula for weight is weight equal to mass time the acceleration due to gravity which is 9.8 m/s2. Weight = mass x gravity

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**IV. Density A. Determining Density**

1. Density is defined as the ratio of mass per unit volume. 2. The calculation for density is the mass divide by the volume of the object. Density = Mass Volume 1. Specific gravity is a comparison of the density of a substance with the density of a reference substance, usually the same temperature. 2. It is measured using a hydrometer. B. Specific Gravity

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**III. Solving Conversion Factors A. Conversion Factors**

1. Whenever two measurements are equivalent, a ratio of the two measurements will equal 1or unity. 2. A ratio of equivalent measurements is called a conversion factor. 3. In a conversion factor, the measurement in the numerator (top) is equivalent to the measurement in the denominator (bottom).

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**III. Solving Conversion Factors A. Conversion Factors**

4. When a measurement is multiplied by a conversion, the numerical value is generally changed, but the actual size of the quantity measured remains the same. 5. Example 60 seconds = 1 minute 1 minute or 60 seconds 60 seconds minute

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**III. Solving Conversion Factors B. Dimensional Analysis**

1. We use problem solving steps to figure out the amount of very small or very big forms of matter. That method is called…… Dimensional Analysis

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**III. Solving Conversion Problems B. Dimensional Analysis**

2. Here is an example: How many eggs can Bug Bunny buy for cupcakes for Elmer Fudd’s birthday if he has $10 to buy eggs with at $0.80 cent for a dozen? First start with what you know 12 eggs = 1 dozen, 6 eggs = ½ dozen Eggs cost ¢80 for 1 dozen Bugs has $10

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**III. Solving Conversion Problems B. Dimensional Analysis**

3. Next we set up Conversion factors 12 eggs/ 1 doz. Or 1 doz./12 eggs $0.80/ 1doz. Or 1 doz./$0.80 Now we can set up the problem $ doz. 12 eggs = 150 eggs $ doz.

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