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## Scientific Measurements

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**BIG NUMBERS**• Scientists often work with very large numbers. • National debt = $5,653,000,000,000 • Bill Gates' net worth = $75,030,000,000 • Distance to Alpha Centauri = 40,120,000,000,000,000 m • Distance to Andromeda Galaxy = 21,800,000,000,000,000,000,000 g • Mass of Sun = 1,990,000,000,000,000,000,000,000,000,000,000 g**Small numbers**• Scientists often work with very small numbers. • Radius of hydrogen atom = 0.000000000052918 m • Mass of Hydrogen atom = 0.0000000000000000000000016733 g • Mass of electron = 0.00000000000000000000000000091096 g**What to do?**• Scientific notation – way of expressing a value as the product of a number between 1 and 10 and a power of 10.**Examples**• 300,000,000 • Move the decimal 8 places to the left • = 3 x 108 • 750,000 • Move the decimal 5 places to the left • = 7.5 x 105**More Practice**• 230,000,000 • 2.3 x 108 • 40,000 • 4 x 104 • 34,000,000 • 3.4 x 107**Scientific Notation cont.**• Scientific notation can also be used to write out very small numbers. • 0.0005 • Move the decimal 4 places to the right • 5 x 10-4**More Practice**• 0.000002 • = 2 x 10-6 • 0.0045 • = 4.5 x 10-3 • 0.000075 • = 7.5 x 10-5**3 x 103**4 x 106 3.4 x 105 2.0 x 104 = 3,000 = 4,000,000 = 340,000 = 20,000 Practice - Reverse**6 x 10-5**4.5 x 10-2 3.5 x 10-3 5.5 x 10-7 = 0.00006 = 0.045 = 0.0035 = 0.00000055 More Practice**Reliability in Measurements**• Precise measurements will give the same results again and again • Accuracy is how close you are to the accepted value**Certainty in Measurement**• Significant digits are those digits that are certain in your measurement plus one estimated • In order to count significant digits just count the digits • 5.6 • 781 • 6,778 • What about large or small numbers?**BIG NUMBERS**• Scientists often work with very large numbers. • National debt = $5,653,000,000,000 • Bill Gates' net worth = $57,030,000,000 • Distance to Alpha Centauri = 40,120,000,000,000,000 m • Distance to Andromeda Galaxy = 21,800,000,000,000,000,000,000 g • Mass of Sun = 1,990,000,000,000,000,000,000,000,000,000,000 g**Small numbers**• Scientists often work with very small numbers. • Radius of hydrogen atom = 0.000000000052918 m • Mass of Hydrogen atom = 0.0000000000000000000000016733 g • Mass of electron = 0.00000000000000000000000000091096 g**Atlantic Pacific Rule**• If decimal is Absent starting from the right count all digits after the 1st non zero • If decimal is Presentstarting from the left count all digits after the 1st non zero**Practice**• 4500 Liters • 0.00543 grams • 0.00607000 seconds • 500,003 meters • 400,000. Joules • 5000340035.000 Amps**Exact Numbers**• Remember that the rules of Sig Figs only apply to measurements and not exact numbers. • Years in a century • Students in a classroom • Centimeters in a meter**Rounding Sig Figs**• Remember to keep the value of the number the same. • Remember to round up if last digit is 5 or more. • Round 12.5 to 2 sig figs • Round 56.99392882 kg to 3 sig figs • Round .00027262299 mL to 4 sig figs • Round 303 meters to 3 sig figs • Round 303 meters to 2 sig figs**Multiplying / Dividing SigFigs**• When multiplying/dividing measurements you are limited by the measurement with the least number of significant digits.**Practice**• Area = L x W • Length = 6.15 m • Width = 4.026 m • Volume = L x W x H • Volume = 3.05 x 2.10 x 0.75**SI Units**• SI units: a revised form of the metric system • SI base units are fundamental units all other units are based upon**Derived units**• Derived units are made from a combination of base units. Examples: • Volume • Density**Converting Metric Units**• SI units based upon factors of 10 • Begin with the prefix given and move the decimal the same number and direction to the desired prefix • Know the prefixes and values: The ones most important for us are Kilo (1,000), Centi (.01) and Milli (.001) Others can be looked up as needed or will be given in the problem.**Practice**• A soda can holds 355 mL convert to L • Convert 76 km to meters • Convert 18 mm to cm • A Thumb drive holds 512 Megabytes convert to Kilobytes • Violet Light has a wavelength of 430 nm convert to km**Ratios**• Ratios are a common way of expressing results in Chemistry • Teacher to student ratio • Velocity • Population Density • Density • Ratios of chemicals in a chemical reaction**Finding Density**• Density = Mass / Volume • Units are (kg/m3) or (g/mL) • Lets calculate Density • Mass = 27 kg • Volume = 3.0 mL • Denstiy = 9.0 kg/mL**More Practice**• Mass = 45 kg • Volume = ???? mL • Density = 5.0 kg/mL**Practice**• Mass = 10.0 g • Volume of water only = 35.0 mL • Volume of water w/ Object = 40.0 mL • Volume of object only = __________ • Density = ______________**Practice**• An aquarium has dimensions of 25.0 cm by 68.5 cm by 34.0 cm. If the mass of the aquarium if 2.3 kg, calculate the density. • The density of air is 0.0013 g/cm3 . How much mass does air have in a volume of 400. cm3?**Water & Density**• Water has a density of 1.0 g/ml at 4o C • Water’s mass in grams is equal to its volume in mL • Any object with a density greater will sink. . . less will float • 1cm3 = 1cc = 1ml**Percent error**There is always some error in your measurement. It is unavoidable.To calculate use the following formula:% Error = ((measured value – accepted value)/ accepted value ) X 100 %or % error = ((O - A)/A ) X 100 %PERCENT ERROR CAN BE NEGATIVE !!!In Science, a negative percent error means your value was less than the accepted value. This is very common in Chemistry.**Practice**• When measuring the density of gold you find a value of 20.9 g/cm3 . The accepted value is 19.3 g/cm3. What is your error ? • Samantha S. Sloppiness measured the volume of her soda before she drank it for her midmorning snack. She measured the volume of the 12 oz. bottle to be 10 oz. What is her error ?**Answers**• # 1 ((20.9 – 19.3) / 19.3 ) x 100 % = 8.29 % Notice it is a positive number since the answer was more than the real value. • # 2 ((10 – 12) / 12 ) x 100 % = - 16.67 % Notice it is a negative number since the answer was less than the real value.