Scientific Measurements

BIG NUMBERS Scientists often work with very large numbers. Scientists often work with very large numbers. National debt = $5,653,000,000,000 National debt = $5,653,000,000,000 Bill Gates' net worth = $57,030,000,000 Bill Gates' net worth = $57,030,000,000 Distance to Alpha Centauri = 40,120,000,000,000,000 m Distance to Alpha Centauri = 40,120,000,000,000,000 m Distance to Andromeda Galaxy = 21,800,000,000,000,000,000,000 g Distance to Andromeda Galaxy = 21,800,000,000,000,000,000,000 g Mass of Sun = 1,990,000,000,000,000,000,000,000,000,000,00 0 g Mass of Sun = 1,990,000,000,000,000,000,000,000,000,000,00 0 g

Small numbers Scientists often work with very small numbers. Scientists often work with very small numbers. Radius of hydrogen atom = m Radius of hydrogen atom = m Mass of Hydrogen atom = g Mass of Hydrogen atom = g Mass of electron = g Mass of electron = 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. 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, ,000,000 Move the decimal 8 places to the left Move the decimal 8 places to the left = 3 x 10 8 = 3 x , ,000 Move the decimal 5 places to the left Move the decimal 5 places to the left = 7.5 x 10 5 = 7.5 x 10 5

More Practice 230,000, ,000, x x ,000 40,000 4 x x ,000,000 34,000, x x 10 7

Scientific Notation cont. Scientific notation can also be used to write out very small numbers. Scientific notation can also be used to write out very small numbers Move the decimal 4 places to the right Move the decimal 4 places to the right 5 x x 10 -4

More Practice = 2 x = 2 x = 4.5 x = 4.5 x = 7.5 x = 7.5 x 10 -5

Practice - Reverse 3 x x x x x x x x 10 4 = 3,000 = 3,000 = 4,000,000 = 4,000,000 = 340,000 = 340,000 = 20,000 = 20,000

More Practice 6 x x x x x x x x = = = = = = = =

Reliability in Measurements Precise measurements will give the same results again and again Precise measurements will give the same results again and again Accuracy is how close you are to the accepted value Accuracy is how close you are to the accepted value

Where would you measure?

Certainty in Measurement Significant digits are those digits that are certain in your measurement plus one estimated Significant digits are those digits that are certain in your measurement plus one estimated In order to count significant digits just count the digits In order to count significant digits just count the digits ,778 6,778 What about large or small numbers? What about large or small numbers?

BIG NUMBERS Scientists often work with very large numbers. Scientists often work with very large numbers. National debt = $5,653,000,000,000 National debt = $5,653,000,000,000 Bill Gates' net worth = $57,030,000,000 Bill Gates' net worth = $57,030,000,000 Distance to Alpha Centauri = 40,120,000,000,000,000 m Distance to Alpha Centauri = 40,120,000,000,000,000 m Distance to Andromeda Galaxy = 21,800,000,000,000,000,000,000 g Distance to Andromeda Galaxy = 21,800,000,000,000,000,000,000 g Mass of Sun = 1,990,000,000,000,000,000,000,000,000,000,00 0 g Mass of Sun = 1,990,000,000,000,000,000,000,000,000,000,00 0 g

Small numbers Scientists often work with very small numbers. Scientists often work with very small numbers. Radius of hydrogen atom = m Radius of hydrogen atom = m Mass of Hydrogen atom = g Mass of Hydrogen atom = g Mass of electron = g Mass of electron = g

Atlantic Pacific Rule If decimal is Absent starting from the right count all digits after the 1 st non zero If decimal is Absent starting from the right count all digits after the 1 st non zero If decimal is Present starting from the left count all digits after the 1 st non zero If decimal is Present starting from the left count all digits after the 1 st non zero

Practice 4500 Liters 4500 Liters grams grams seconds seconds 500,003 meters 500,003 meters 400,000. Joules 400,000. Joules Amps Amps

Exact Numbers Remember that the rules of Sig Figs only apply to measurements and not exact numbers. Remember that the rules of Sig Figs only apply to measurements and not exact numbers. Years in a century Years in a century Students in a classroom Students in a classroom Centimeters in a meter Centimeters in a meter

Rounding Sig Figs Remember to keep the value of the number the same. Remember to keep the value of the number the same. Remember to round up if last digit is 5 or more. Remember to round up if last digit is 5 or more. –Round 12.5 to 2 sig figs –Round kg to 3 sig figs –Round 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. When multiplying/dividing measurements you are limited by the measurement with the least number of significant digits.

Practice Area = L x W Area = L x W Length = 6.15 m Length = 6.15 m Width = m Width = m Volume = L x W x H Volume = L x W x H Volume = 3.05 x 2.10 x 0.75 Volume = 3.05 x 2.10 x 0.75

SI Units SI units: a revised form of the metric system SI units: a revised form of the metric system SI base units are fundamental units all other units are based upon SI base units are fundamental units all other units are based upon

Base Units Physical QuantityName of SI unitSymbol for SI unit lengthmeterm masskilogramkg timeseconds electric currentampereA temperatureKelvinK amount of substancemolemol luminous intensitycandelacd

Derived units Derived units are made from a combination of base units. Derived units are made from a combination of base units.Examples: Volume Volume Density Density

Examples of SI derived units expressed in terms of base units Derived quantity SI derived unit NameSymbol area square metre m2m2m2m2 volume cubic metre m3m3m3m3 speed, velocity metre per second m/s acceleration metre per second squared m/s 2 wavenumber 1 per metre m -1 density, mass density kilogram per cubic metre kg/m 3 specific volume cubic metre per kilogram m 3 /kg current density ampere per square metre A/m 2 magnetic field strength ampere per metre A/m

Converting Metric Units SI units based upon factors of 10 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 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. 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 A soda can holds 355 mL convert to L Convert 76 km to meters Convert 76 km to meters Convert 18 mm to cm Convert 18 mm to cm A Thumb drive holds 512 Megabytes convert to Kilobytes A Thumb drive holds 512 Megabytes convert to Kilobytes Violet Light has a wavelength of 430 nm convert to km Violet Light has a wavelength of 430 nm convert to km

Ratios Ratios are a common way of expressing results in Chemistry Ratios are a common way of expressing results in Chemistry Teacher to student ratio Teacher to student ratio Velocity Velocity Population Density Population Density Density Density Ratios of chemicals in a chemical reaction Ratios of chemicals in a chemical reaction

Finding Density Density = Mass / Volume Density = Mass / Volume Units are (kg/m 3 ) or (g/mL) Units are (kg/m 3 ) or (g/mL) Lets calculate Density Lets calculate Density Mass = 27 kg Mass = 27 kg Volume = 3.0 mL Volume = 3.0 mL Denstiy = 9.0 kg/mL Denstiy = 9.0 kg/mL

More Practice Mass = 45 kg Mass = 45 kg Volume = ???? mL Volume = ???? mL Density = 5.0 kg/mL Density = 5.0 kg/mL

Practice Mass = 10.0 g Mass = 10.0 g Volume of water only = 35.0 mL Volume of water only = 35.0 mL Volume of water w/ Object = 40.0 mL Volume of water w/ Object = 40.0 mL Volume of object only = __________ Volume of object only = __________ Density = ______________ 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 g/cm 3. How much mass does air have in a volume of 400. cm 3 ?

Water & Density  Water has a density of 1.0 g/ml at 4 o C  Water’s mass in grams is equal to its volume in mL  Any object with a density greater will sink... less will float  1cm 3 = 1cc = 1ml

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. Percent error

Practice When measuring the density of gold you find a value of 20.9 g/cm 3. The accepted value is 19.3 g/cm 3. What is your error ? When measuring the density of gold you find a value of 20.9 g/cm 3. The accepted value is 19.3 g/cm 3. 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 % # 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 % = % # 2((10 – 12) / 12 ) x 100 % = % Notice it is a negative number since the answer was less than the real value.