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Standards of Measurements Chapter 1.2

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Accuracy and Precision Accuracy – how close a measured value is to the actual value Precision – how close the measured values are to each other

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Significant Figures All nonzero digits are significant. 1, 2, 3, 4, 5, 6, 7, 8, 9 Zeros within a number are always significant. Both 4308 and 40.05 have four significant figures.

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Significant Figures Zeros that set the decimal point are not significant. 470,000 has two significant figures. Trailing zeros that aren't needed to hold the decimal point are significant. 4.00 has three significant figures.

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Significant Figures If the least precise measurement in a calculation has three significant figures, then the calculated answer can have at most three significant figures. Mass = 34.73 grams Volume = 4.42 cubic centimeters. Rounding to three significant figures, the density is 7.86 grams per cubic centimeter.

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Scientific Notation For large numbers, moving the decimal to the left will result in a positive number 346500 = 3.46 x 10 5 For small numbers, moving the decimal to the right will result in a negative number 0.000145 = 1.45 x 10 -4 For numbers less than 1 that are written in scientific notation, the exponent is negative.

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Scientific Notation Before numbers in scientific notation can be added or subtracted, the exponents must be equal. 5.32 x 10 5 + 9.22 x 10 4 5.32 x 10 5 + 0.922 x 10 5 5.32 + 0.922 x 10 5 6.24 x 10 5

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Scientific Notation When numbers in scientific notation are multiplied, only the number is multiplied. The exponents are added. (3.33 x 10 2 ) (2.71 x 10 4 ) (3.33) (2.71) x 10 2+4 9.02 x 10 6

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Scientific Notation When numbers in scientific notation are divided, only the number is divided. The exponents are subtracted. 4.01 x 10 9 1.09 x 10 2 4.01 x 10 9-2 1.09 3.67 x 10 7

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Scientific Notation A rectangular parking lot has a length of 1.1 × 10 3 meters and a width of 2.4 × 10 3 meters. What is the area of the parking lot? (1.1 x 10 3 m) (2.4 x 10 3 m) (1.1 x 2.4) (10 3+3 ) (m x m) 2.6 x 10 6 m 2

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SI Units Kilo- (k) 1000 Milli- (m) Hecto- (h) Deka- (da) Base Unit Deci- (d) Centi- (c) 100 10 m, L, g 0.1 0.01 0.001 Mnemonic device: King Henry Died By Drinking Chocolate Milk

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Metric System Meter (m) – The basic unit of length in the metric system Length – the distance from one point to another A meter is slightly longer than a yard

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Metric System Liter (L) – the basic unit of volume in the metric system A liter is almost equal to a quart

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Metric System Gram (g) – The basic unit of mass

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Derived Units Combination of base units Volume – length width height 1 cm 3 = 1 mL Density – mass per unit volume (g/cm 3 ) D = MVMV D M V

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Density 1) An object has a volume of 825 cm 3 and a density of 13.6 g/cm 3. Find its mass. GIVEN: V = 825 cm 3 D = 13.6 g/cm 3 M = ? WORK : M = DV M = 13.6 g x 825 cm 3 cm 3 1 M = 11,220 g D M V

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Density 2) A liquid has a density of 0.87 g/mL. What volume is occupied by 25 g of the liquid? GIVEN: D = 0.87 g/mL V = ? M = 25 g D M V WORK : V = M D V = 25 g 0.87 g/mL V = 28.7 mL

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Density 3) You have a sample with a mass of 620 g & a volume of 753 cm 3. Find the density. GIVEN: M = 620 g V = 753 cm 3 D = ? D M V WORK : D = M V D = 620 g 753 cm 3 D = 0.82 g/cm 3

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Unit Factors

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Slopes

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Percentage Error

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Temperature A degree Celsius is almost twice as large as a degree Fahrenheit. You can convert from one scale to the other by using one of the following formulas:

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Temperature Convert 90 degrees Fahrenheit to Celsius o C = 5/9 ( o F - 32) o C = 5/9 (90 - 32) o C = 0.55555555555555556 (58) o C = 32.2

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Temperature Convert 50 degrees Celsius to Fahrenheit o F = 9/5 ( o C ) + 32 o F = 9/5 (50 ) + 32 o F = 1.8 (50) + 32 o F = 90 + 32 o F = 122

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Temperature The SI base unit for temperature is the kelvin (K). A temperature of 0 K, or 0 kelvin, refers to the lowest possible temperature that can be reached. In degrees Celsius, this temperature is –273.15°C. To convert between kelvins and degrees Celsius, use the formula:

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Temperature

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