# 0.4 1.5 physical quantities and units  (Page 4/17)

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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:

$80\overline{)\text{m}}×\frac{\text{1 km}}{1000\overline{)\text{m}}}=0\text{.080 km.}$

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.

Click [link] for a more complete list of conversion factors.

Approximate values of length, mass, and time
Lengths in meters Masses in kilograms (more precise values in parentheses) Times in seconds (more precise values in parentheses)
${\text{10}}^{-\text{18}}$ Present experimental limit to smallest observable detail ${\text{10}}^{-\text{30}}$ Mass of an electron ${\text{10}}^{-\text{23}}$ Time for light to cross a proton
${\text{10}}^{-\text{15}}$ Diameter of a proton ${\text{10}}^{-\text{27}}$ Mass of a hydrogen atom ${\text{10}}^{-\text{22}}$ Mean life of an extremely unstable nucleus
${\text{10}}^{-\text{14}}$ Diameter of a uranium nucleus ${\text{10}}^{-\text{15}}$ Mass of a bacterium ${\text{10}}^{-\text{15}}$ Time for one oscillation of visible light
${\text{10}}^{-\text{10}}$ Diameter of a hydrogen atom ${\text{10}}^{-5}$ Mass of a mosquito ${\text{10}}^{-\text{13}}$ Time for one vibration of an atom in a solid
${\text{10}}^{-8}$ Thickness of membranes in cells of living organisms ${\text{10}}^{-2}$ Mass of a hummingbird ${\text{10}}^{-8}$ Time for one oscillation of an FM radio wave
${\text{10}}^{-6}$ Wavelength of visible light $\text{1}$ Mass of a liter of water (about a quart) ${\text{10}}^{-3}$ Duration of a nerve impulse
${\text{10}}^{-3}$ Size of a grain of sand ${\text{10}}^{2}$ Mass of a person $\text{1}$ Time for one heartbeat
$\text{1}$ Height of a 4-year-old child ${\text{10}}^{3}$ Mass of a car ${\text{10}}^{5}$ One day $\left(8\text{.}\text{64}×{\text{10}}^{4}\phantom{\rule{0.25em}{0ex}}\text{s}\right)$
${\text{10}}^{2}$ Length of a football field ${\text{10}}^{8}$ Mass of a large ship ${\text{10}}^{7}$ One year (y) $\left(3\text{.}\text{16}×{\text{10}}^{7}\phantom{\rule{0.25em}{0ex}}\text{s}\right)$
${\text{10}}^{4}$ Greatest ocean depth ${\text{10}}^{\text{12}}$ Mass of a large iceberg ${\text{10}}^{9}$ About half the life expectancy of a human
${\text{10}}^{7}$ Diameter of the Earth ${\text{10}}^{\text{15}}$ Mass of the nucleus of a comet ${\text{10}}^{\text{11}}$ Recorded history
${\text{10}}^{\text{11}}$ Distance from the Earth to the Sun ${\text{10}}^{\text{23}}$ Mass of the Moon ${\text{10}}^{\text{17}}$ Age of the Earth
${\text{10}}^{\text{16}}$ Distance traveled by light in 1 year (a light year) ${\text{10}}^{\text{25}}$ Mass of the Earth ${\text{10}}^{\text{18}}$ Age of the universe
${\text{10}}^{\text{21}}$ Diameter of the Milky Way galaxy ${\text{10}}^{\text{30}}$ Mass of the Sun
${\text{10}}^{\text{22}}$ Distance from the Earth to the nearest large galaxy (Andromeda) ${\text{10}}^{\text{42}}$ Mass of the Milky Way galaxy (current upper limit)
${\text{10}}^{\text{26}}$ Distance from the Earth to the edges of the known universe ${\text{10}}^{\text{53}}$ Mass of the known universe (current upper limit)

## Unit conversions: a short drive home

Suppose that you drive the 10.0 km from your university to home in 20.0 min. Calculate your average speed (a) in kilometers per hour (km/h) and (b) in meters per second (m/s). (Note: Average speed is distance traveled divided by time of travel.)

#### Questions & Answers

what is math number
Tric Reply
x-2y+3z=-3 2x-y+z=7 -x+3y-z=6
Sidiki Reply
Need help solving this problem (2/7)^-2
Simone Reply
x+2y-z=7
Sidiki
what is the coefficient of -4×
Mehri Reply
-1
Shedrak
the operation * is x * y =x + y/ 1+(x × y) show if the operation is commutative if x × y is not equal to -1
Alfred Reply
An investment account was opened with an initial deposit of $9,600 and earns 7.4% interest, compounded continuously. How much will the account be worth after 15 years? Kala Reply lim x to infinity e^1-e^-1/log(1+x) given eccentricity and a point find the equiation Moses Reply 12, 17, 22.... 25th term Alexandra Reply 12, 17, 22.... 25th term Akash College algebra is really hard? Shirleen Reply Absolutely, for me. My problems with math started in First grade...involving a nun Sister Anastasia, bad vision, talking & getting expelled from Catholic school. When it comes to math I just can't focus and all I can hear is our family silverware banging and clanging on the pink Formica table. Carole I'm 13 and I understand it great AJ I am 1 year old but I can do it! 1+1=2 proof very hard for me though. Atone hi Adu Not really they are just easy concepts which can be understood if you have great basics. I am 14 I understood them easily. Vedant find the 15th term of the geometric sequince whose first is 18 and last term of 387 Jerwin Reply I know this work salma The given of f(x=x-2. then what is the value of this f(3) 5f(x+1) virgelyn Reply hmm well what is the answer Abhi If f(x) = x-2 then, f(3) when 5f(x+1) 5((3-2)+1) 5(1+1) 5(2) 10 Augustine how do they get the third part x = (32)5/4 kinnecy Reply make 5/4 into a mixed number, make that a decimal, and then multiply 32 by the decimal 5/4 turns out to be AJ how Sheref can someone help me with some logarithmic and exponential equations. Jeffrey Reply sure. what is your question? ninjadapaul 20/(×-6^2) Salomon okay, so you have 6 raised to the power of 2. what is that part of your answer ninjadapaul I don't understand what the A with approx sign and the boxed x mean ninjadapaul it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared Salomon I'm not sure why it wrote it the other way Salomon I got X =-6 Salomon ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6 ninjadapaul oops. ignore that. ninjadapaul so you not have an equal sign anywhere in the original equation? ninjadapaul hmm Abhi is it a question of log Abhi 🤔. Abhi I rally confuse this number And equations too I need exactly help salma But this is not salma it's Faiza live in lousvile Ky I garbage this so I am going collage with JCTC that the of the collage thank you my friends salma Commplementary angles Idrissa Reply hello Sherica im all ears I need to learn Sherica right! what he said ⤴⤴⤴ Tamia hii Uday hi salma hi Ayuba Hello opoku hi Ali greetings from Iran Ali salut. from Algeria Bach hi Nharnhar A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place. Kimberly Reply Jeannette has$5 and \$10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
August Reply
What is the expressiin for seven less than four times the number of nickels
Leonardo Reply
How do i figure this problem out.
how do you translate this in Algebraic Expressions
linda Reply
why surface tension is zero at critical temperature
Shanjida
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
s.
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
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Source:  OpenStax, Kinematics. OpenStax CNX. Sep 11, 2015 Download for free at https://legacy.cnx.org/content/col11878/1.5
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