SOLUTION: How do you graph & compare real numbers and find the absolute value of real numbers?
Algebra.Com
Question 752581: How do you graph & compare real numbers and find the absolute value of real numbers?
Answer by KMST(5328) (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:
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
and .
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:
, , , .
Positive numbers are to the right of zero, so they are less than zero:
, , , .
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,
with is unit to the left of zero.
with is units to the left of zero.
PRACTICAL TIPS:
To figure out where to place a number like or you can calculate an approximate value as a decimal.
= -8.571428571428571428571428571428....
so you can use (rounded) to figure out where to plot that value.
The point for must be units to the left of zero. That's a distance a litle longer than units, so you place it a little to the left of the point that is halfway between -8 and -9.
(rounded)
Your calculator may give you the result of that calculation as , and you know that it is an irrational number with infinite non-repeating digits, but for your purposes, is a good approximation, accurate enough.
So, when graphing by hand, you plot the point for at a distance of about units to the left of zero. You can pretend that is
= -3.333333333... and plot = approximately of a unit to the left of .
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