Mathematics units

Ryan$

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Hi guys ; I know exactly what units are in math but still confused a lil about something which is: lets assume that cm is the less ultimate unit to measure destination; and we know that one KM is 1000 Meter and 1000 Meter is 1000*100cm , but now how can I convert cm to number to be able to assign it in 1000*100cm? I mean if I have any less ultimate unit in terms of measurement, doesn't it represent a number?

in abbreviation, a units at math basically are also numbers? if so, then how can I represent cm as number?(because I already assume that cm is the less ultimate measurement) .. I'm trying to explain that is it right to say that units are basically representing amount of numbers?
 
With units you are actually treading close to Physics. Which is just fine with me. :cool:

But you have to stick with the conventions. "m" is meters. "k" is kilo. So "kilometers" is km, not KM. Both Math and Physics are "case-sensitive."

A quantity is a number with a unit attached, so what we are doing is looking for different ways to express quantities. We transform one quantity in one unit to the same quantity in a different unit by multiplying by 1. For example, say we need to transform 4 km to m. Then
\(\displaystyle \left ( \frac{4 ~ km}{1} \right ) = \left ( \frac{4 ~ km}{1} \right ) \cdot \left ( \dfrac{1000 ~ m}{1 ~ km} \right ) = 4 \times 1000 ~ m\)

(The factor 1000 m / 1 km is simply equal to 1 so we aren't really changing anything.)

To get 4 km to cm we can do this twice (assuming you don't recall off the top of your head how many cm are in a km.)
\(\displaystyle \left ( \frac{4 ~ km}{1} \right ) = \left ( \frac{4 ~ km}{1} \right ) \cdot \left ( \dfrac{1000 ~ m}{1 ~ km} \right ) \cdot \left ( \dfrac{100 ~ cm}{1 ~ m} \right ) = 4 \times 1000 \times 100 ~ cm\)

Notice how the various units cancel.

-Dan
 
Hi guys,
I want to ask if I have an equation and I solved its elements with units "cm" and I after solving it I got x=5cm ;
my question is , if I convert the result x to meter i.e x= 5/100 ; will I get the same result(same x in meter) if I solve the equation with unit meter? if yes, then why?



thanks in advance.
 
yes, you will. Changing the original problem from cm to m is equivalent to dividing every number by 100 and that does not change the answer to the problem just as dividing both sides of an equation does by 100 does not change the solution of the equation.
 
I want to ask if I have an equation and I solved its elements with units "cm" and I after solving it I got x=5cm ;
my question is , if I convert the result x to meter i.e x= 5/100 ; will I get the same result(same x in meter) if I solve the equation with unit meter? if yes, then why?

You could think of it as a change of variables. If x is the length in centimeters, and y is the length in meters, then x = 100y. You are in effect replacing x with 100y in the equation, and solving for y.

If that is not clear, try it! That's the best to ask "Can I?" or "Why can I?" questions. Solve the equation both ways, and compare. Since we don't have your equation, we can't do this for you; but it's better for you to do it anyway.
 
yes, you will. Changing the original problem from cm to m is equivalent to dividing every number by 100 and that does not change the answer to the problem just as dividing both sides of an equation does by 100 does not change the solution of the equation.


May I ask over here, why we need to define at all units in math? I mean lets assume that cm is the less measurement unit then if I write 5[cm] I can't convert it more? what I'm going to explain that if I have 5[km]=5*1000[m]=5*1000*100[cm] then I can't convert more .. my question "cm" doesn't consider an amount ?! for example maybe cm is about value "10" then they stated that this value will be defined as cm ??! thanks for helping .
 
You could think of it as a change of variables. If x is the length in centimeters, and y is the length in meters, then x = 100y. You are in effect replacing x with 100y in the equation, and solving for y.

If that is not clear, try it! That's the best to ask "Can I?" or "Why can I?" questions. Solve the equation both ways, and compare. Since we don't have your equation, we can't do this for you; but it's better for you to do it anyway.


thanks !

May I ask over here, why we need to define at all units in math? I mean lets assume that cm is the less measurement unit then if I write 5[cm] I can't convert it more? what I'm going to explain that if I have 5[km]=5*1000[m]=5*1000*100[cm] then I can't convert more .. my question "cm" doesn't consider an amount ?! for example maybe cm is about value "10" then they stated that this value will be defined as cm ??! thanks for helping

what I'm going to ask if I reached the least ultimate measurement unit then I can't convert it to any less units because I already reached the less ultimate unit .... so I'm asking then I can assume the that the less ultimate unit is considered as "amount" but defined as "specific label like cm" ? thanks
 
I'm trying to understand if we can convert unit from unit , then if I've reached a least unit , is the least unit basically represented a number ?
 
I'm trying to understand if we can convert unit from unit , then if I've reached a least unit , is the least unit basically represented a number ?
6 centimeters is a length, not a number. Numbers are ideas.

Are 3 chickens numbers or birds?

2 cars will take eight people on a trip, but no numbers will take anyone on a trip.

When you convert units to a new unit, you are still dealing with units.

1 meter = 100 centimeters. Units are on both sides of the equation.
 
6 centimeters is a length, not a number. Numbers are ideas.

Are 3 chickens numbers or birds?

2 cars will take eight people on a trip, but no numbers will take anyone on a trip.

When you convert units to a new unit, you are still dealing with units.

1 meter = 100 centimeters. Units are on both sides of the equation.

I'm with you that 6 centimeters is a length not a number, but if I assume that centimeters is the least ultimate measurement , then how can I convert it to numbers? I mean if I have 5 cm, then it says that the length is 5cm but what's cm? 5 is a number and how long/amount of one cm? thanks
 
Maybe you guys still didn't understand me, I'm trying to say that how much/far is the least ultimate measurement measure related to area? because at the end units are about numbers/amounts...........
 
Maybe you guys still didn't understand me, I'm trying to say that how much/far is the least ultimate measurement measure related to area? because at the end units are about numbers/amounts...........

1) There is no such thing as a "least ultimate measurement". Feel free to let this idea vanish into the mists.
2) 5 cm is 5 cm. If you convert it to m ==> 5 cm = 0.05 m, it's still 5 cm. It cannot be converted to a number.
3) If you COULD convert 5 cm into a number... {Incantation: Lengthus be Numberus (in a mysterious voice)}... you would be changing its very nature and there would be no going back. Frankly, I don't want you doing this with my petrol. If I put 40 litres (10.6 US Gallons) of petrol in my tank, I can drive around the city, but if you come along and turn my fuel into a number, my driving will end quite abruptly.
4) Early mathematicians spent some time hoping something like a "least ultimate measurement" existed. Alas, there never was such a discovery or invention.
5) It seems likely that we are not understanding your question. Since it seems to make no sense, what chance have we of understanding it?
6) Question: If you call a dog's tails a leg, how many legs does the dog have?
 
Maybe you guys still didn't understand me, I'm trying to say that how much/far is the least ultimate measurement measure related to area? because at the end units are about numbers/amounts...........
In what subject - are you getting into these "existential" questions? Particle Physics?
 
Maybe you guys still didn't understand me, I'm trying to say that how much/far is the least ultimate measurement measure related to area? because at the end units are about numbers/amounts...........
No, it is not true that at the end units are about numbers/amounts. Maybe at the end units are about a number of units. Units are simply not numbers. End of discussion. I loved physics because there was a built in check to confirm that what you did was wrong or probably correct. That check was units. For example in the end you got velocity, v = 5meters/sec2 you know you made a mistake! Let units be your friend instead of just thinking they are numbers.
 
No, it is not true that at the end units are about numbers/amounts. Maybe at the end units are about a number of units. Units are simply not numbers. End of discussion. I loved physics because there was a built in check to confirm that what you did was wrong or probably correct. That check was units. For example in the end you got velocity, v = 5meters/sec2 you know you made a mistake! Let units be your friend instead of just thinking they are numbers.

Indeed. Units will save you. Please don't wish them out of existence.
 
I got the point behind using units, thanks guys very cooperative !!
 
Hi guys, whenever I have sec/sec then sec/sec=1
what's confusing me, how from splitting units we get number?! I mean we don't have numbers ..so how we get number?! really weird magic
 
Hi guys, whenever I have sec/sec then sec/sec=1
what's confusing me, how from splitting units we get number?! I mean we don't have numbers ..so how we get number?! really weird magic
The "1" is not really a number. It's an identity meaning that it's a "blank" unit. It's rather like adding 0 to a number: the number doesn't change when you add the 0 to it. Similarly if we multiply a unit by sec/sec the unit doesn't change.

-Dan
 
WHAAAAT?????????????????????????????????????????????????????????????! impossible, so 1 is a magic?
 
Just divide out the units, and avoid what you think right now of as "magic."

Suppose I know my hourly rate of pay in dollars per hour, and I know the total number of hours I worked. Then my total pay is the product of the two quantities, where the hours cancel (are divided out), and I'm left with dollars as the only unit, which is dimensionally consistent.

Once you get more experience under your belt, you will begin to develop an understanding of what seems odd to you now. As you learn what to do, and how to do it, the understanding of why it works will come naturally. If you try to pick apart everything before you have that experience, you're only going to frustrate yourself.
 
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