# Converting within the metric system | Pre-Algebra | Khan Academy

Convert 51.8 decimeters
to kilometers. So let’s just think about what
decimeters means in terms of meters, and then we can think
about what kilometers mean in terms of meters, and
then convert them. So we’re going to start
with 51.8 decimeters. Now, as a starting point, just
to keep things simple, we’re going to convert them into
meters, because this prefix tells us a lot about how
many meters this is. So if we want to convert it
into meters, our units are going to have to be meters
per decimeter. And we need this because this
decimeter and that decimeter are going to cancel out, and
we’re going to be just left with meters. Now 1 meter is how
many decimeters? Well, the prefix deci
means 1/10. So 1 decimeter is
1/10 of a meter. Or another way of thinking
about it is there are 10 decimeters for every meter. This is a smaller unit. 10 of these make up 1 of these,
or 1/10 of a meter per decimeter, which is exactly
what that is telling you. 1/10 of a meter. Now if you multiply these two
things, what do we get? Well, the decimeters cancel out,
and we divide 51.8 by 10. Multiplying by 1/10 is the same
thing as dividing by 10. So this is going to be equal
to 51.8 divided by 10. The decimal’s just going
to move to the left. It’s going to be 5.18. So this is going to
be 5.18 meters. And you should always
do a reality check. Did it make sense? Does it make sense that
51 decimeters are equal to 5 meters? Well, sure. It should go down. We’re going from a smaller unit
to a larger unit, so we should have fewer of that larger
unit to make the same distance in this case. A meter is a unit of length. Now, we’re at 5.18 meters, and
we want to now convert it to kilometers. So we’re going to want meters
in the denominator and kilometers in the numerator. Why? Because this meter and that
meter will cancel out. Now, how many meters make
up a kilometer? The kilo tells us 1,000. That is 1,000 meters. So 1,000 meters are equal
to 1 kilometer. So if we were to multiply this,
the meters cancel out and we’ll just be left
with kilometers. And multiplying something by
1/1,000 is the exact same thing as dividing by 1,000,
and that makes sense. We should get a smaller number
here because we’re going from a smaller unit to
a larger unit. So we’re going to need
a much smaller amount of the larger unit. So this is going to be equal
to 5.18/1,000 kilometers. Now, the easy way to do this,
if we take 5.18/10 is equal to– we just move the decimal
one to the left. It’s going to be
equal to 0.518. If we take 5.18 and divide it
by 100, we’re going to take the decimal two to the left. So one, two, we’re going to
have to add a zero here. So it’s going to be 0.0518. And if we take 5.18 and we
divide by 1,000, we’re going to move the decimal
three to the left. So we’ll just do it. So if we start with 5.18– the
decimal started here– we’re going to go one, two,
so that’s one zero, and then three. And that’s where the decimal
is going to sit there. So this is Or another way, this
is a little over 5/1,000. This right here is 5/1,000. It’s a little bit
more than that. So our final answer: 51.8
decimeters is equal to 0.00518 kilometers. And always do a reality check. Does that make sense? Well, sure. We’re going from a really small
unit here, a bunch of a small unit, to a very small
amount of a large unit. It makes sense. It makes sense that this number
goes down while the actual unit becomes larger.

### 40 thoughts on “Converting within the metric system | Pre-Algebra | Khan Academy”

• September 6, 2010 at 11:43 pm
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King Henry died monday drinking chocklate milk

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• September 9, 2010 at 12:55 am
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Thanks sooo much!!!! For this video!

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• September 9, 2010 at 12:59 am
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What about significant digit?

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• September 13, 2010 at 5:07 am
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@XLyeeb that only applies if it were chemistry.

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• February 17, 2011 at 10:53 pm
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@Tyncidog we do king henry unexpectedly died drinking chocolate milke!!

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• January 23, 2012 at 1:21 pm
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@healbyGod im glade i found this while im still in college

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• January 23, 2012 at 1:23 pm
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Just incase anyone is wondering the secret to college. Just get a job with the school, they drop the price to almost nothing. YW

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• July 8, 2012 at 11:16 am
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You're a geographical characteristic that you found this…? How are you even in college?!?

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• August 5, 2012 at 4:15 am
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lol what??!? How am i in college? Well to start i make can speak

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• August 30, 2012 at 10:43 pm
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Thank you so much for the vid. You just helped me so much. Keep up the work!

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• September 13, 2012 at 2:27 am
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khan acedemy!!!!!!

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• September 19, 2012 at 3:07 am
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i didn't understand……..hm

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• November 23, 2012 at 5:05 pm
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This explanation makes it harder then it has to be IMO. Just move the decimal point. There are a few other videos here on Youtube which do it right.

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• February 4, 2013 at 2:17 am
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boring and stupid

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• April 18, 2013 at 11:53 am
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excellent

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• August 9, 2013 at 1:35 pm
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All of a sudden this all made sense! Thank you!

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• September 2, 2013 at 10:47 am
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Thank you very much

now It suddenly make sense

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• September 8, 2013 at 10:54 am
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You are a symbol of pure education.

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• October 15, 2013 at 11:23 pm
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my teacher taught us a way with adding 0's but I like this way a lot better !

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• January 3, 2014 at 5:49 pm
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Awesome!!!! Love Khan Academy! Keep up the good work.

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• September 3, 2014 at 7:18 pm
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where did the 100 come from?

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• May 16, 2015 at 11:46 am
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thanks

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• November 10, 2015 at 2:56 pm
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math and science yo (^-^)*the more you know

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• November 10, 2015 at 2:56 pm
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but probily not on youtube srry

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• March 24, 2016 at 2:42 pm
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I was 223 like

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• November 30, 2016 at 7:28 pm
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and subscribe

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• January 29, 2017 at 10:53 pm
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This makes it way more complicated…

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• February 25, 2017 at 12:29 pm
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Thank you Khan! I´m really starting to understand after this video!

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• March 13, 2017 at 4:37 pm
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I don't understand…

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• March 14, 2017 at 3:04 am
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like si estas por la maestra de ingles

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• September 20, 2017 at 8:19 pm
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+Khan Academy this makes no sense

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• February 15, 2018 at 11:36 pm
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khan ac5d3m9 4 lif3

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• March 9, 2018 at 9:07 pm
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That is the wrong answer if you do not believe me go search a unit converter.

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• March 12, 2018 at 11:24 pm
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Thanks for the help Khan!!!

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• September 20, 2018 at 11:58 pm
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Thanks for no help 👎🏽😐😑😥😥😭

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• April 22, 2019 at 10:40 pm
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i love it

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• May 19, 2019 at 7:23 pm
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All over the place

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• September 9, 2019 at 8:57 pm
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Thanks alot

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• January 16, 2020 at 3:33 pm
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Wow thanks for the vid keep up the good work and have fun

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