Why is -10 smaller than -100? My physics teacher told me recently that -10 is less than -100.
The way I look at it is in 2 ways: 


*

*Having minus £100 would mean you have less money that if you had -£10.

*If you are presented with a number spectrum ranging from -100 to 100, it is clear that -100 is lowest down the spectrum and therefore lower/less that -10.


So is there any valid explanation as to why is -10 less than -100?
 A: I think your physics teacher is mistaken. -100 is unquestionably less than -10, because $-100 < -10$. If you owe \$100 you have less money than someone who owes only \$10.
However, -100 is bigger than -10, because if you owe \$100 you owe a bigger amount than someone who owes only \$10.
Addendum: Some commenters have claimed that "-100 is unquestionably less than -10, because $-100 < -10$" is tautological. It is not. The first clause concerns the meaning of the English-language phrase "less than", which is what the original question was asking about.  The second clause concerns the formal mathematical statement that $-100 < -10$. I am asserting that the phrase "less than" is normally understood to mean the mathematical relation denoted by "$<$". The conventional reading of "$<$" as "less than" or "is less than" supports this claim. In contrast, in the following paragraph I am claiming that the meaning of the English-language phrase "is bigger than" (and implicitly, "is smaller than") is not modeled by the mathematical $<$ relation. (More precisely, it is modeled by $<$ only for non-negative quantities.)
These claims might be false, or poorly supported by evidence, but they are not tautological. I hope this clears things up.
A: Your teacher is wrong or you misheard him/her.  $x < y$ means $x$ is to the left of $y$ on the number line, when $x$ and $y$ are real numbers.  Since $-100$ is to the left of $-10$, $-100 < -10$.
If you want to talk about magnitude, then you're comparing absolute values, i.e., the distance from $0$.  In that case, we're comparing $|-100| = 100$ and $|-10| = 10$.  And, $10 < 100$ so $|-10| < |-100|$.  But, if that is what you are talking about, you would need to mention something about magnitude or distance from $0$.
A: It isn't, plain and simple. -100 is less than -10, i.e. -10 is larger than -100. Generally, $x$ is less than $y$ ($x < y$) if $x-y$ is negative.
Since $(-100) - (-10) = -100 + 10 = -90$ is negative, $-100$ is less than $-10$.
Your physics teacher was wrong, or he defined a non-standard less-than operation on the integers first. If you define your own meaning of less-than, you can obviously make it behave arbitrarily. Whether or not such a definition has any value is a different question, though.
A: By definition we say that a number $x$ is less than a number $y$ if the number $y - x$ is positive. So with $x = -100$ and $y= -10$ we have that $y - x = 90 > 0$, so by definition $-100$ is less than $-10$.
I am guessing that your teacher had different definition. You might want to ask a physics.stackexchange.com about whether such a definition would exist for some physics problem.
A: There is an easier way to see this (not using inequality). We say that $x$ is less than $y$ if there is a positive number $z$ such that $y=x+z$ (in fact this is the definition of $x < y$ for real numbers).
In this case you can say $-100$ is less than $-10$ because there is a positive number $z$ such that $-10=-100+z$, of course $z = 90$.
A: As far as physics is concerned, it is a matter of context. Sometimes, negative numbers are just part of a scale, as I am sure that your teacher would agree that -100°C is less than -10°C and sometimes, negative numbers are a way of indicating directions, a negative current is actually just a positive current in another direction. The problem disappears if you leave the 1-dimensional world and note that the first kind of quantities are scalar and the second kind of quantities are vectors. 
One can employ a more precise language than your teacher, but there is no ambiguity in context. It is not useful to insist on unnecessarily formal terminology.
