MeasurementsChapter 2

ConversionsQuantity English unit abb SI unit abb Definition

massPoundsounces

lbsoz gram g

amount of matter in an object

volumeGallonquart

galqt liter L

amount of space an object occupies

lengthInches, feet Yards, miles

in ftyd mi meter m

distance between two objects

time seconds

HrSmin Seconds s finite duration

temperature Fahrenheit ºFKelvinCelsius

K ºC

how hot or cold something is

amount ofsubstance N/A N/A mole mol

the amount of a substance

Based on the Power of 10

King Henry Died By drinking chocolate milkKilo 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 Practice1. 3.68kg = _________g

2. 568cm = _________m

3. 8700mL = _________L

4. 25mg = _________g

5. 0.101cm = ______mm

6. 250mL = _________L

7. 600g = _________kg

8. 8900mm = _______m

9. 0.000004m =

____mm

10. 0.250kg = _______mg

Answers

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)

1. Exact Numbers: may be counted or defined.

1. Are absolutely accurate2. People in a room.

2. There is some uncertainty in measurements.

3. Sig. Figs. Indicate the uncertainty in the measurements.

1. Digits believed to be correct by those that makes them

2. 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 FIGS1. Zeros (0) used only to position the

decimal are not significant.1. 0.0000593 3 sig figs2. 23000 depends on the measurement

RULES FOR SIG FIGS

2. In x/÷, an answer contains no more sig figs than the least # of sig figs used in the operation.

1. ie: (12.34 cm)*(1.23 cm) = 15.1782 cm2

Correct answer =15.2 cm2

RULES FOR SIG FIGS

1. In +/- the last digit retained in the answer is determined by the position of the first estimated number.

2. In other words

1. (37.24+10.3)=47.5447.52. (27.87-

21.2342)=6.63586.64

Measurements: Sig Figs

Sec 2-3

• Only measurements are given significance.− There are some numbers that aren’t

considered in terms of significance.o Conversion factors have an infinite number

of significant figures (ratios of equal measures, like 1 ft/12 in or 60 sec/1 min)

o Exact numbers also have an infinite number of significant figures, like 20 apples or 10 test tubes

9.0 km

Your Turn…• How many significant figures does each

of the following measurements have?

21000 g 1505 btu 30.0024 sec 21.040 amps 40.000 625 000 kg 6

Pg 44-57

Measurements: Sig Figs

Sec 2-3

• 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

1. Calculate the area of a crystal surface that measures 1.34 m by 0.7488 m.

2. Calculate how many minutes a project took if the times spent on it each day were 92.5 min, 33.32 min, 25.0 min, 45 min, and 95.33 min.

3. Calculate how many hours the result from #2 would work out to be.

Your Turn…• Carry out each of the mathematical

operation.

1.00 m, 291 min, 4.85 hrs

1. 32,700

Your Turn…• Write the following #’s in sci notation…

3.27 x 104

2. 1,024,0003. 0.004 7100

1.024 x 106

4.7100 x 10-3

Pg 44-57Sec 2-3

2nd function button you push

before the EE button

The EE button is 2nd function of the

comma button

Avoid this button like the plague

4.587E4/1.2E-338225000

Use this button to enter a negative

number

ScientificNotation

On theCalculator█

Derived Units

1. Units that are made up of 2+ basic units, ie. Velocity, force, acceleration.

1. Density1. Amount of mass per unit volume.2. D=m/v3. Unites are g/cm3 or g/mL or g/L4. Cm3 is a unit of volume for solids because v=l*w*h

cm*cm*cm=cm3

2. Example: A 47.23 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 H2O=1.00g/ml@25 degrees C

› No units

How to: Derived Units

1. Read problems2. Write formula3. Write variables4. Plug in numbers5. Solve

1. For example: Express the density of mercury in lb/ft3 if the density if 13.59 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

English to Metric

Conversions  

length

2.54cm=1in39.37in=1m1.609km=1mi

volume1L=1.057qt28.32L=1cubic foot

mass

453.6g=1lb1g=0.03527oz1 metric ton=1.102 standard tonnes

Dimensional Analysis Problems

1. 74cm=__________in2. 25mL=__________tsp3. 50kg=__________lbs4. 160km=__________mi5. 3.6L=__________gal6. 500kg=__________oz7. 100m=__________yds

Dimensional Analysis Answers

1. 29in or 2.9*101in2. 5.1tsp3. 1*102lbs4. 9.94*101mi5. 9.5*10-1gal6. 1.76*104oz7. 1.09*102yds8. 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.