# 1.6 Mathematical treatment of measurement results  (Page 3/9)

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## Computing quantities from measurement results and known mathematical relations

(a) What (average) fuel economy, in miles per gallon, did the Roadster get during this trip?

(b) If gasoline costs $3.80 per gallon, what was the fuel cost for this trip? ## Solution (a) We first convert distance from kilometers to miles: $\text{1250 km}\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}\frac{\text{0.62137 mi}}{\text{1 km}}\phantom{\rule{0.2em}{0ex}}=\text{777 mi}$ and then convert volume from liters to gallons: $213\phantom{\rule{0.2em}{0ex}}\overline{)\text{L}}\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}\frac{\text{1.0567}\phantom{\rule{0.2em}{0ex}}\overline{)\text{qt}}}{1\phantom{\rule{0.2em}{0ex}}\overline{)\text{L}}}\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}\frac{\text{1 gal}}{4\phantom{\rule{0.2em}{0ex}}\overline{)\text{qt}}}\phantom{\rule{0.2em}{0ex}}=\text{56.3 gal}$ Then, $\text{(average) mileage}=\phantom{\rule{0.2em}{0ex}}\frac{\text{777 mi}}{\text{56.3 gal}}\phantom{\rule{0.2em}{0ex}}=\text{13.8 miles/gallon}=\text{13.8 mpg}$ Alternatively, the calculation could be set up in a way that uses all the conversion factors sequentially, as follows: $\frac{1250\phantom{\rule{0.2em}{0ex}}\overline{)\text{km}}}{213\phantom{\rule{0.2em}{0ex}}\overline{)\text{L}}}\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}\frac{\text{0.62137 mi}}{1\phantom{\rule{0.2em}{0ex}}\overline{)\text{km}}}\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}\frac{1\phantom{\rule{0.2em}{0ex}}\overline{)\text{L}}}{\text{1.0567}\phantom{\rule{0.2em}{0ex}}\overline{)\text{qt}}}\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}\frac{4\phantom{\rule{0.2em}{0ex}}\overline{)\text{qt}}}{\text{1 gal}}=\text{13.8 mpg}$ (b) Using the previously calculated volume in gallons, we find: $\text{56.3 gal}\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}\frac{\text{3.80}}{\text{1 gal}}=\text{214}$ ## Check your learning A Toyota Prius Hybrid uses 59.7 L gasoline to drive from San Francisco to Seattle, a distance of 1300 km (two significant digits). (a) What (average) fuel economy, in miles per gallon, did the Prius get during this trip? (b) If gasoline costs$3.90 per gallon, what was the fuel cost for this trip?

(a) 51 mpg; (b) \$62

## Conversion of temperature units

We use the word temperature to refer to the hotness or coldness of a substance. One way we measure a change in temperature is to use the fact that most substances expand when their temperature increases and contract when their temperature decreases. The mercury or alcohol in a common glass thermometer changes its volume as the temperature changes. Because the volume of the liquid changes more than the volume of the glass, we can see the liquid expand when it gets warmer and contract when it gets cooler.

To mark a scale on a thermometer, we need a set of reference values: Two of the most commonly used are the freezing and boiling temperatures of water at a specified atmospheric pressure. On the Celsius scale, 0 °C is defined as the freezing temperature of water and 100 °C as the boiling temperature of water. The space between the two temperatures is divided into 100 equal intervals, which we call degrees. On the Fahrenheit    scale, the freezing point of water is defined as 32 °F and the boiling temperature as 212 °F. The space between these two points on a Fahrenheit thermometer is divided into 180 equal parts (degrees).

Defining the Celsius and Fahrenheit temperature scales as described in the previous paragraph results in a slightly more complex relationship between temperature values on these two scales than for different units of measure for other properties. Most measurement units for a given property are directly proportional to one another (y = mx). Using familiar length units as one example:

$\text{length in feet}=\left(\frac{\text{1 ft}}{\text{12 in.}}\right)\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}\text{length in inches}$

where y = length in feet, x = length in inches, and the proportionality constant, m, is the conversion factor. The Celsius and Fahrenheit temperature scales, however, do not share a common zero point, and so the relationship between these two scales is a linear one rather than a proportional one (y = mx + b). Consequently, converting a temperature from one of these scales into the other requires more than simple multiplication by a conversion factor, m, it also must take into account differences in the scales’ zero points (b).

wat are hydrocarbon s
I think they are molecules that comprise only of hydrogen and carbon atoms ( they are organic if I'm not mistaken)
Mmathabo
am new here can I join
Yeko
yes u can
Benita
give two properties of liquid
molecules are slightly packed and they follow the shape of a container.
Obedie
what is measurement
is the comparison of an unknown quantity with a fixed quantity of the same kind
How does an element differ from a compound? How are they similar?
an element is an indivisible particles that can take part in a reaction and consist of smaller or tiny particles i.e proton, neutrons and electron while a compound is when two or more element chemically combine together. They are similar when they are homogeneous compound. they take the same rxn.
Yusuf
an element is s chemically pure substance containing a particular type of atoms.. A COMPOUND is a substance containing atoms from different elements..
Inemesit
How to get the Lewis formula of SeCl+3
hi,I'm new here can I join the conversation
EZEA
what is the structural formula for starch
Starch is a mixture (of chemicals) of amylose and amylopectin. Both are macromolecules and polymers. You can search on wikipedia.
Abdelkarim
what is the roles of filter bed
Fathmat
what is the roles of Alu m
Fathmat
what is the roles of chlorine
Fathmat
Roles can be classified or correlate it to different areas: For example: Chlorine can be used in reactions (in industry) to manufacture HCl, which then can be used for other things. Or in swimming pools to kill bacteria. Or as a component in compounds with pharmaceutical roles (drugs). For Al:
Abdelkarim
Its dentisty value is suitable to be used in alloys (mixture of metals) in aircraft bodies. Also, Aluminium foils, Tin cans,.. Some of them are also in Al overhead cables in streets and long roads.
Abdelkarim
what is chemistry
Maxamed
what is the meaning of exceedingly
it is an adverb which means extremely
Rohini
what is atomic chemistry?
Lewis structure for no3
Lewis structure for no3
Yes
Gillian
Lewis structure for no3
Nomvelo
what is weak acid
It is an acid which partially ionises in water.
Abdelkarim
what is incandescence
Clifton
what makes it glow
Clifton
why is it red, irange and yellow in color
Clifton
hello am new here and I want to join you
Aliyu
hello
Clifton
hi
Aliyu
too
Gillian
hello i am new here please i want to join this group
Paul
Hi, I'm also new here
Salaudeen
Hi
Keeya
hello guys !!
Sourav
what is pressure?
The force applied to suction Area of the body
Ahmed
Matter composed of exceedingly small paticle called atom.
Yushao
questions related to metals
occurrence and preparation of the representatives metals
Regina
list the 20, periodic table and their symbols
hydrogen:h helium;he lithium:l beryllium:be Boron:b Carbon;C Nitrogen:n Oxygen:O FLUORINE:f Neon:n Sodium:s Magnesium:mg Aluminum:a Silicon:s Phosphorus:p Sulphur:s Chlorine:c Argon;a Potassium:p Calcium:c
Benita
Hydrogen, helium, lithium, beryllium, boron, carbon, nitrogen, oxygen, fluorine, neon, sodium, magnesium, aluminium, silicon, phosphorus, sulphur, chlorine, argon, potassium, calcium
Cudjoe
Welcome
Gillian
there are 118 known elements ...you numbnuts
what is a solute
Any substance that is disolved in a liqid solvent to create a solution
Fifa
sorry liquid
Fifa
it's a liquid substance
Fathmat
hello group
Ayomide
is the substance that dissolves in the solvent
Amos
so is HCl ionic compound
No, covalent compound ➡️ molecule. As both H and Cl are non-metals and and form covalent bind by sharing valence e-. But can fully ionice in water forming H+ (a proton, a reason for acidity) and Cl- (anion =Chloride) Hydrogen Chloride is a gas at room; Hydrochloric acid = HCl (aq), dissolved in w
Abdelkarim
Form covalenr bond*
Abdelkarim
The question marks are an emoji in the first sentence is an unread emoji. HCl Covalent compund -> molecule
Abdelkarim
Hi.
Queen
Hi
Calvin
Yh
Cudjoe
yes
Amos
what is chemistry
is the study of composition of substances and the way they behave under different conditions
Amos
how do calculate n1 though n6 any help on understanding the concept
Clifton
is the study of properties of matter and it's component
Grace