# Measurements Chapter 2.

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Measurements Chapter 2

Conversions Quantity English unit abb SI unit Definition
mass Pounds ounces lbs oz gram g amount of matter in an object volume Gallon quart gal qt liter L amount of space an object occupies length Inches, feet Yards, miles in ft yd mi meter m distance between two objects time seconds Hr S min Seconds s finite duration temperature Fahrenheit ºF Kelvin Celsius K ºC how hot or cold something is amount of substance N/A mole mol the amount of a substance

Based on the Power of 10 106 M 109 G 1012 T micro 10-6 μ nano 10-9 n
King Henry Died By drinking chocolate milk Kilo Hecta Deca base deci centi milli 1000 100 10 1 0.1 0.01 0.001 10^3 10^2 10^1 10^0 10^-1 10^-2 10^-3 MEGA 106 M micro 10-6 μ GIGA 109 G nano 10-9 n TERA 1012 T pico 10-12 p

Conversion Practice 3.68kg = _________g 600g = _________kg
568cm = _________m 8900mm = _______m 8700mL = _________L m = ____mm 25mg = _________g 0.250kg = _______mg 0.101cm = ______mm 250mL = _________L

Accuracy v. Precision Accuracy- How close a measured value agrees w/ the correct value Precision-How close ea. Measurement agrees w/ ea. other

Which of the measuring devices would provide
a more accurate measurement? Why is this one a better device to use for measuring? Sec 2-3 Pg 44-57

Sig Figs(a) Exact Numbers: may be counted or defined.
Are absolutely accurate People in a room. There is some uncertainty in measurements. Sig. Figs. Indicate the uncertainty in the measurements. Digits believed to be correct by those that makes them Can only report ONE estimated digit.

Using Scientific Measurements
Using a calibrated instrument of measure you can be certain of the accuracy of some of the digits measured. The last digit of the measurement is however, always questionable Excluding the last digit would be misleading With the last digit you have some indication of the value’s likely range Any measurement reported should consist of the certain digits plus the uncertain digit. The last digit is uncertain, but it isn’t insignificant…

Sec 2-3 Pg 44-57

Using Scientific Measurements
Since only the significant digits are reported it is important to be able to determine all the significant digits in a measurement. There are a set of rules that allow us to determine the significance of any figures in any measurement even if we don’t know the origin of the measurement

RULES FOR SIG FIGS Zeros (0) used only to position the decimal are not significant.  3 sig figs 23000  depends on the measurement

RULES FOR SIG FIGS Correct answer =15.2 cm2
2. In x/÷, an answer contains no more sig figs than the least # of sig figs used in the operation. ie: (12.34 cm)*(1.23 cm) = cm2 Correct answer =15.2 cm2

RULES FOR SIG FIGS (37.24+10.3)=47.5447.5 (27.87-21.2342)=6.63586.64
In +/- the last digit retained in the answer is determined by the position of the first estimated number. In other words ( )=47.5447.5 ( )=6.63586.64

Measurements: Sig Figs
Only measurements are given significance. There are some numbers that aren’t considered in terms of significance. Conversion factors have an infinite number of significant figures (ratios of equal measures, like 1 ft/12 in or 60 sec/1 min) Exact numbers also have an infinite number of significant figures, like 20 apples or 10 test tubes Sec 2-3

Your Turn… How many significant figures does each of the following measurements have? 2 9.0 km 1 1000 g 3 505 btu 2 sec 4 1.040 amps kg 6

Measurements: Sig Figs
Just because the calculated answer in your calculator has 8 digits in the answer – doesn’t mean they are all significant Answers calculated from measurements may not be expressed with more significant digits than any of the original measure ments Calculator answers must be rounded to reflect the least accurate measurement Sec 2-3 Pg 44-57

Carry out each of the mathematical operation.
Your Turn… Carry out each of the mathematical operation. Calculate the area of a crystal surface that measures 1.34 m by m. Calculate how many minutes a project took if the times spent on it each day were 92.5 min, min, 25.0 min, 45 min, and min. Calculate how many hours the result from #2 would work out to be. 1.00 m, 291 min, 4.85 hrs

Your Turn… Write the following #’s in sci notation… 3.27 x 104 32,700 1.024 x 106 1,024,000 x 10-3

Scientific On the Notation Calculator Sec 2-3 Pg 44-57 4.587E4/1.2E-3
On the Calculator 2nd function button you push before the EE button Avoid this button like the plague The EE button is 2nd function of the comma button Use this button to enter a negative number Sec 2-3 Pg 44-57

Derived Units Units that are made up of 2+ basic units, ie. Velocity, force, acceleration. Density Amount of mass per unit volume. D=m/v Unites are g/cm3 or g/mL or g/L Cm3 is a unit of volume for solids because v=l*w*h  cm*cm*cm=cm3 Example: A mL sample of ethanol has a mass of 37.32g. What is its density? (hint: denisty= mass/volume)

Derived Units Specific Gravity
Ratio of a substance’s density to the density of H2O Density of degrees C No units

How to: Derived Units Read problems Write formula Write variables
Plug in numbers Solve For example: Express the density of mercury in lb/ft3 if the density if g/cm3.

Your Turn… A block of Zinc metal has the dimensions 5.0 cm X 7.0 cm X 20.0 cm, and its mass is 5.0 kg. What is the density of the Zinc metal in g/mL? Zinc’s density is 7.13 g/cm3, what is the percent error from the lab?

Dimensional Analysis Also called the factor label method
Easy way to convert between English and SI (metric). Uses equivalent amounts 12 in = 1 ft = 12in/1ft 38m=______________ft.

More conversions length volume mass English to Metric Conversions
length 2.54cm=1in 39.37in=1m 1.609km=1mi volume 1L=1.057qt 28.32L=1cubic foot mass 453.6g=1lb 1g= oz 1 metric ton=1.102 standard tonnes

Dimensional Analysis Problems
74cm=__________in 25mL=__________tsp 50kg=__________lbs 160km=__________mi 3.6L=__________gal 500kg=__________oz 100m=__________yds

29in or 2.9*101in 5.1tsp 1*102lbs 9.94*101mi 9.5*10-1gal 1.76*104oz 1.09*102yds Example 2: 8.484*102lbs/ft3

% Error %Error = (Actual-Theoretical) ___________________ * 100 Theoretical Will be Θ if the accepted value is greater. (+) if the accepted value is less.

Problems Express 12gal in cm3.
Suppose Mrs. Fraga’s Bentley contains a gas tank (handmade) that holds up to 16 gal of fuel. The price of gas is \$0.315 per Liter (obviously not a problem). How much would Mrs. Fraga need to charge on her AmEx Platinum for one full tank of gas? Does not include tip.