SOLUTION: How do you graph & compare real numbers and find the absolute value of real numbers?

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Question 752581: How do you graph & compare real numbers and find the absolute value of real numbers?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
To graph and compare real numbers you just plot them on a number line, like this:

number_line%28+600%2C+-10%2C+10%2C+-1%2C+sqrt%283%29%2C+6.5%2C+-60%2F7%2C1-sqrt%2819%29+%29

The number line is like a ruler, with positive and negative integers marked at regular intervals. Negative numbers are to the left of zero, positive numbers are to the right of zero.
TIP: That is easier to do with paper that already has regularly spaced markings. Grid paper is a good choice. Paper with lines works well if you turn the paper so that the lines run up and down rather than side to side.

COMPARING:
The numbers to the left are smaller than (less than) the numbers to the right, so
1-sqrt%2819%29%3C-1 and sqrt%283%29%3C6.5.
You can turn that around and say that a number than is to the right is larger (greater) than all the numbers to its left.
Negative numbers are to the left of zero, so they are less than zero:
-9%3C0, -60%2F7%3C0, 1-sqrt%2819%29%3C0, -1%3C0.
Positive numbers are to the right of zero, so they are less than zero:
2%3E0, sqrt%283%29%3E0, 6.5%3E0, 8%3E0.

ABSOLUTE VALUE:
Negative numbers are to the left of zero, positive numbers are to the right of zero.
The absolute value of a number is the distance between the number and zero in the graph, and It is always a positive number.
For example,
-1 with abs%28-1%29=1 is 1 unit to the left of zero.
-60%2F7 with abs%28-60%2F7%29=60%2F7 is 60%2F7=8%261%2F7 units to the left of zero.

PRACTICAL TIPS:
To figure out where to place a number like -60%2F7 or 1-sqrt%2819%29 you can calculate an approximate value as a decimal.
-60%2F7= -8.571428571428571428571428571428....
so you can use -60%2F7=-8.6 (rounded) to figure out where to plot that value.
The point for -60%2F7 must be 8.6 units to the left of zero. That's a distance a litle longer than 8.5=8%261%2F2 units, so you place it a little to the left of the point that is halfway between -8 and -9.
1-sqrt%2819%29=-3.36 (rounded)
Your calculator may give you the result of that calculation as 3.358898944, and you know that it is an irrational number with infinite non-repeating digits, but for your purposes, -3.36 is a good approximation, accurate enough.
So, when graphing by hand, you plot the point for 1-sqrt%2819%29 at a distance of about 3.36 units to the left of zero. You can pretend that -3.36 is
-3%261%2F3= -3.333333333... and plot 1-sqrt%2819%29= approximately-3.36 1%2F3 of a unit to the left of -3.