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**Measurement & Calculations**

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Biblical Reference He measured its wall and it was 144 cubits thick, by man's measurement, which the angel was using. Revelation 21:17

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**Accuracy vs. Precision For a single measurement:**

Accuracy - An indication of how close a measurement is to the accepted value Precision - An indication of the degree of exactness of a measurement For multiple measurements: Accuracy - An indication of how close the average measurement is to the accepted value Precision - An indication of the agreement among a number of similar measurements

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**Accuracy – measurement of closeness to the true value of a number**

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**Precision – measure of how close a series of measurements are to one another**

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**Scientific Notation: 602,000,000,000,000,000,000,000 copper atoms**

6.02 x 1023 copper atoms grams 3.27 x grams Only 1 digit to the left of the decimal place.

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Significant Figures: When you make a measurement there is some estimation Recorded numbers in a measurement or calculation are called significant figures What is the length of the black line in cm? How many significant figures are in the measurement?

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**Number of Significant Figures = 2**

You can't always keep all the digits a calculator produces. You can only keep the significant ones, the ones that are not beyond the accuracy of the measuring device. These digits are called significant digits or figures. Length cm Number of Significant Figures = 2

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**Significant Figure Rules :**

Non zeros count (123.34) – 5 Sig Figs 2. Leading zeros do NOT count (0.004) – 1 Sig Fig 3. Captive zeros count (2004, 2.004, 20.04) – 4 Sig Figs 4. Trailing zeros count IF there is a decimal point (20., 20.00, 0.200) – 2, 4, and 3 Sig Figs

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**Significant Figures in Calculations:**

A calculated answer cannot be more precise than the least precise measurement from which it was calculated Rounding If the last number is less than 5, round down If the last number is greater than 5, round up If the last number is a 5, round so that the rounded number is even.

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**Mathematical Operations:**

Rounding with Addition and Subtraction Round to the least number of decimal places Example: = 11.0 Rounding with Multiplication and Division Round to the same number of significant figures as the measurement with the least number of significant figures Example: 540. g / 62 ml = 8.7 g/ml

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Determining Error: Accepted value – correct value based on reliable references Experimental value – value measured in lab Error = Accepted Value – Experimental value Percent Error = |Error| x 100 Accepted Value *|Error| is the absolute value of the error

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**SI units Measurements are fundamental to the experimental sciences**

Science uses the International System of Measurements (SI) MKS and CGS

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**Measuring with SI Units - MKS**

Quantity SI Base Unit Symbol Length meter m Mass kilogram kg Temperature Kelvin K Time second s Amount of substance mole mol Luminous intensity candela cd Electric current ampere A

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**Metric Prefixes Prefix Meaning Factor mega (M)**

1 million times larger than preceding 106 kilo (k) 1000 times larger than preceding 103 deci (d) 10 times smaller than preceding 10-1 centi (c) 100 times smaller than preceding 10-2 milli (m) 1000 times smaller than preceding 10-3 micro (m) 1 million times smaller than preceding 10-6 nano (n) 1 billion times smaller than preceding 10-9 pico (p) 1 trillion times smaller than preceding 10-12

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**Metric Units of Length Unit Relationship Example Kilometer (km)**

1 km = 103 m Five city blocks Meter (m) Base unit Height of doorknob Decimeter (dm) 101 dm = 1 m Large orange Centimeter (cm) 102 cm = 1 m Shirt button Millimeter (mm) 103 mm = 1 m Thickness of dime Micrometer (mm) 106 mm = 1 m Diameter of bacteria Nanometer (nm) 109 nm = 1 m Thickness of RNA

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**Metric Units of Mass & Volume**

Relationship Example Kilogram (kg) 1 kg = 103 g Small textbook Gram (g) 1 g = 10-3 kg Dollar bill Milligram (mg) 103 mg = 1 g Sugar cube Microgram (mg) 106 mg = 1 g Single salt crystal Unit Relationship Example Liter (L) Base unit Quart of milk Milliliter (mL) 103 mL = 1 L 20 water drops Cubic centimeter (cm3) 1 cm3 = 1 mL Sugar cube Microliter (mL) 106 mL = 1 L Single salt crystal

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**Standard Kilogram Height = 3.9 cm Diameter = 3.9 cm**

Platinum-Iridium Cylinder

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**Metric Units of Temperature**

The Celsius scale sets the freezing point of water at 0°C and the boiling point at 100°C. The Kelvin scale sets 0 at absolute zero. The units of Kelvin and Celsius are equivalent K = °C °C = K –

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**Metric Units of Energy 1 Joule (J)= 0.2390 calories (cal)**

1 calorie (cal) = Joules (J) One calorie is the amount of heat that raises the temperature of 1 g of pure water by 1 ° C

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Derived Units

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Derived Units

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A conversion factor is a ratio that, when multiplied by the item you are converting, cancels out the units you do not want and leaves you with the units you want. Dimensional Analysis is a technique where you use the dimensions/units to check if a relationship is correct.

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**Everyday Conversion Factors**

1 dollar 4 quarters 10 dimes 20 nickels 100 pennies

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**Metric Conversion Factors**

1 meter 10 decimeters 101 100 centimeters 102 1,000 millimeters 103 1,000,000 micrometers 106 1,000,000,000 nanometers 109

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**Conversion Factor Steps**

Step 1 – Determine what units you are given and what units you need. Step 2 – Determine what conversion factors you need to use. Step 3 – Arrange the conversion factors so that the units you do not want cancel out. Step 4 – Make sure your last unit is the unit need.

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**Conversion Examples 500 cm ´ 1 m = 5 m 100 cm 6 cm ´ 10 mm = 60 mm**

8 h 60 min 60 sec = 28,800 s 1 h 1 min

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**Example Problem With sig figs**

K2 is the world’s second tallest peak at 8000 m. What is the height of K2 in feet? With sig figs

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**Dimensional Analysis Question**

The period (T) of oscillation of a simple pendulum depends upon the acceleration of gravity(g) and the length (L) of the pendulum. Which expression below represents the relationship between T, g and L?

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**Dimensional Analysis Question**

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**Coordinate Systems - Cartesian**

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**Coordinate Systems - Polar**

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**Density Density = Mass / Volume**

A cm3 sample of platinum has a density of 21.4 g/cm3. What is its mass?

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**Comparative Densities**

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Chapter 3 Scientific Measurement

Chapter 3 Scientific Measurement

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