Is -1 less than 0.1? In a High School Maths Test, I presumed that since -1 has as much mathematical mass as a whole unit [-1 x -1 = 1, 1 x 1 = 1] and 0.1 represents one tenth of a unit, that -1 is greater than 0.1
-1 is to the left of 0.1 on a number line but does that make it lesser than 0.1?
Clearly, the teacher believed I was wrong but inexplicably so and no marking comments to help me.  Can someone please help me to explain the difference?  
 A: If it is $-1^\circ C$ outside, it is colder (and not warmer)  than with $0.1^\circ C$. If your bank balance shows $-1\$$ you are poorer (and not richer) than with $0.1\$$. Best you think of the number line with negatives to the left, positives to the right. Then "less than" is the same as "to the left of".
A: If we add $1$ to both, we obtain $-1+1=0$ and $0.1+1=1.1$ and it's clear that $0<1.1$.  (We can picture this as "shifting" the number line by $1$.)
What you seem to be getting confused with is that $-1$ is greater in magnitude than $0.1$.  It's true that $|-1|>|0.1|$.
A: "Greater than" isn't really about size, or, as you put it, "mathematical mass". It's about position on the number line. The number line extends towards $-\infty$ on the left and towards $\infty$ on the right, and $a>b$ if and only if $a$ is strictly to the right of $b$ on the number line.
The idea that you have of measuring the size of a number so that $-1$ is "bigger" than $0.1$ is exactly what the absolute value function does. The number $|a|$ is the distance between $a$ and $0$, which is a good way to think about its, I don't know, "length". So then $|-1|>|0.1|$. But the question on your exam wasn't about absolute values, so unfortunately your teacher is right this time around.
