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1.2 Physical quantities and units  (Page 4/18)

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Metric prefixes for powers of 10 and their symbols
Prefix Symbol Value See Appendix A for a discussion of powers of 10. Example (some are approximate)
exa E 10 18 size 12{"10" rSup { size 8{"18"} } } {} exameter Em 10 18  m size 12{"10" rSup { size 8{"18"} } " m"} {} distance light travels in a century
peta P 10 15 size 12{"10" rSup { size 8{"15"} } } {} petasecond Ps 10 15  s size 12{"10" rSup { size 8{"15"} } " s"} {} 30 million years
tera T 10 12 size 12{"10" rSup { size 8{"12"} } } {} terawatt TW 10 12  W size 12{"10" rSup { size 8{"12"} } `W} {} powerful laser output
giga G 10 9 size 12{"10" rSup { size 8{9} } } {} gigahertz GHz 10 9  Hz size 12{"10" rSup { size 8{9} } `"Hz"} {} a microwave frequency
mega M 10 6 size 12{"10" rSup { size 8{6} } } {} megacurie MCi 10 6  Ci size 12{"10" rSup { size 8{6} } `"Ci"} {} high radioactivity
kilo k 10 3 size 12{"10" rSup { size 8{3} } } {} kilometer km 10 3  m size 12{"10" rSup { size 8{3} } " m"} {} about 6/10 mile
hecto h 10 2 size 12{"10" rSup { size 8{2} } } {} hectoliter hL 10 2  L size 12{"10" rSup { size 8{2} } " L"} {} 26 gallons
deka da 10 1 size 12{"10" rSup { size 8{1} } } {} dekagram dag 10 1  g size 12{"10" rSup { size 8{1} } `g} {} teaspoon of butter
— — 10 0 size 12{"10" rSup { size 8{0} } } {} (=1)
deci d 10 − 1 size 12{"10" rSup { size 8{ - 1} } } {} deciliter dL 10 − 1  L size 12{"10" rSup { size 8{ - 1} } `L} {} less than half a soda
centi c 10 − 2 size 12{"10" rSup { size 8{ - 2} } } {} centimeter cm 10 − 2  m size 12{"10" rSup { size 8{ - 2} } `m} {} fingertip thickness
milli m 10 − 3 size 12{"10" rSup { size 8{ - 3} } } {} millimeter mm 10 − 3  m size 12{"10" rSup { size 8{ - 3} } `m} {} flea at its shoulders
micro µ 10 − 6 size 12{"10" rSup { size 8{ - 6} } } {} micrometer µm 10 − 6  m size 12{"10" rSup { size 8{ - 6} } `m} {} detail in microscope
nano n 10 − 9 size 12{"10" rSup { size 8{ - 9} } } {} nanogram ng 10 − 9  g size 12{"10" rSup { size 8{ - 9} } `g} {} small speck of dust
pico p 10 − 12 size 12{"10" rSup { size 8{ - "12"} } } {} picofarad pF 10 − 12  F size 12{"10" rSup { size 8{ - "12"} } F} {} small capacitor in radio
femto f 10 − 15 size 12{"10" rSup { size 8{ - "15"} } } {} femtometer fm 10 − 15  m size 12{"10" rSup { size 8{ - "15"} } `m} {} size of a proton
atto a 10 − 18 size 12{"10" rSup { size 8{ - "18"} } } {} attosecond as 10 − 18  s size 12{"10" rSup { size 8{ - "18"} } `s} {} time light crosses an atom

Known ranges of length, mass, and time

The vastness of the universe and the breadth over which physics applies are illustrated by the wide range of examples of known lengths, masses, and times in [link] . Examination of this table will give you some feeling for the range of possible topics and numerical values. (See [link] and [link] .)

A magnified image of tiny phytoplankton swimming among the crystal of ice.[
Tiny phytoplankton swims among crystals of ice in the Antarctic Sea. They range from a few micrometers to as much as 2 millimeters in length. (credit: Prof. Gordon T. Taylor, Stony Brook University; NOAA Corps Collections)
A view of Abell Galaxy with some bright stars and some hot gases.
Galaxies collide 2.4 billion light years away from Earth. The tremendous range of observable phenomena in nature challenges the imagination. (credit: NASA/CXC/UVic./A. Mahdavi et al. Optical/lensing: CFHT/UVic./H. Hoekstra et al.)

Unit conversion and dimensional analysis

It is often necessary to convert from one type of unit to another. For example, if you are reading a European cookbook, some quantities may be expressed in units of liters and you need to convert them to cups. Or, perhaps you are reading walking directions from one location to another and you are interested in how many miles you will be walking. In this case, you will need to convert units of feet to miles.

Let us consider a simple example of how to convert units. Let us say that we want to convert 80 meters (m) to kilometers (km).

The first thing to do is to list the units that you have and the units that you want to convert to. In this case, we have units in meters and we want to convert to kilometers .

Next, we need to determine a conversion factor    relating meters to kilometers. A conversion factor is a ratio expressing how many of one unit are equal to another unit. For example, there are 12 inches in 1 foot, 100 centimeters in 1 meter, 60 seconds in 1 minute, and so on. In this case, we know that there are 1,000 meters in 1 kilometer.

Now we can set up our unit conversion. We will write the units that we have and then multiply them by the conversion factor so that the units cancel out, as shown:

80 m × 1 km 1000 m = 0 .080 km. size 12{"80"" m" times { {"1 km"} over {"1000 m"} } =0 "." "080"`"km"} {}

Note that the unwanted m unit cancels, leaving only the desired km unit. You can use this method to convert between any types of unit.

Questions & Answers

how did you get 1640
Noor Reply
If auger is pair are the roots of equation x2+5x-3=0
Peter Reply
Wayne and Dennis like to ride the bike path from Riverside Park to the beach. Dennis’s speed is seven miles per hour faster than Wayne’s speed, so it takes Wayne 2 hours to ride to the beach while it takes Dennis 1.5 hours for the ride. Find the speed of both bikers.
MATTHEW Reply
420
Sharon
from theory: distance [miles] = speed [mph] × time [hours] info #1 speed_Dennis × 1.5 = speed_Wayne × 2 => speed_Wayne = 0.75 × speed_Dennis (i) info #2 speed_Dennis = speed_Wayne + 7 [mph] (ii) use (i) in (ii) => [...] speed_Dennis = 28 mph speed_Wayne = 21 mph
George
Let W be Wayne's speed in miles per hour and D be Dennis's speed in miles per hour. We know that W + 7 = D and W * 2 = D * 1.5. Substituting the first equation into the second: W * 2 = (W + 7) * 1.5 W * 2 = W * 1.5 + 7 * 1.5 0.5 * W = 7 * 1.5 W = 7 * 3 or 21 W is 21 D = W + 7 D = 21 + 7 D = 28
Salma
Devon is 32 32​​ years older than his son, Milan. The sum of both their ages is 54 54​. Using the variables d d​ and m m​ to represent the ages of Devon and Milan, respectively, write a system of equations to describe this situation. Enter the equations below, separated by a comma.
Aaron Reply
find product (-6m+6) ( 3m²+4m-3)
SIMRAN Reply
-42m²+60m-18
Salma
what is the solution
bill
how did you arrive at this answer?
bill
-24m+3+3mÁ^2
Susan
i really want to learn
Amira
I only got 42 the rest i don't know how to solve it. Please i need help from anyone to help me improve my solving mathematics please
Amira
Hw did u arrive to this answer.
Aphelele
hi
Bajemah
-6m(3mA²+4m-3)+6(3mA²+4m-3) =-18m²A²-24m²+18m+18mA²+24m-18 Rearrange like items -18m²A²-24m²+42m+18A²-18
Salma
complete the table of valuesfor each given equatio then graph. 1.x+2y=3
Jovelyn Reply
x=3-2y
Salma
y=x+3/2
Salma
Hi
Enock
given that (7x-5):(2+4x)=8:7find the value of x
Nandala
3x-12y=18
Kelvin
please why isn't that the 0is in ten thousand place
Grace Reply
please why is it that the 0is in the place of ten thousand
Grace
Send the example to me here and let me see
Stephen
A meditation garden is in the shape of a right triangle, with one leg 7 feet. The length of the hypotenuse is one more than the length of one of the other legs. Find the lengths of the hypotenuse and the other leg
Marry Reply
how far
Abubakar
cool u
Enock
state in which quadrant or on which axis each of the following angles given measure. in standard position would lie 89°
Abegail Reply
hello
BenJay
hi
Method
I am eliacin, I need your help in maths
Rood
how can I help
Sir
hmm can we speak here?
Amoon
however, may I ask you some questions about Algarba?
Amoon
hi
Enock
what the last part of the problem mean?
Roger
The Jones family took a 15 mile canoe ride down the Indian River in three hours. After lunch, the return trip back up the river took five hours. Find the rate, in mph, of the canoe in still water and the rate of the current.
cameron Reply
Shakir works at a computer store. His weekly pay will be either a fixed amount, $925, or $500 plus 12% of his total sales. How much should his total sales be for his variable pay option to exceed the fixed amount of $925.
mahnoor Reply
I'm guessing, but it's somewhere around $4335.00 I think
Lewis
12% of sales will need to exceed 925 - 500, or 425 to exceed fixed amount option. What amount of sales does that equal? 425 ÷ (12÷100) = 3541.67. So the answer is sales greater than 3541.67. Check: Sales = 3542 Commission 12%=425.04 Pay = 500 + 425.04 = 925.04. 925.04 > 925.00
Munster
difference between rational and irrational numbers
Arundhati Reply
When traveling to Great Britain, Bethany exchanged $602 US dollars into £515 British pounds. How many pounds did she receive for each US dollar?
Jakoiya Reply
how to reduced echelon form
Solomon Reply
Jazmine trained for 3 hours on Saturday. She ran 8 miles and then biked 24 miles. Her biking speed is 4 mph faster than her running speed. What is her running speed?
Zack Reply
d=r×t the equation would be 8/r+24/r+4=3 worked out
Sheirtina
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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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