document.write( "Question 752581: How do you graph & compare real numbers and find the absolute value of real numbers?
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #457964 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
To graph and compare real numbers you just plot them on a number line, like this:
\n" ); document.write( "
\n" ); document.write( " $\"number_line%28+600%2C+-10%2C+10%2C+-1%2C+sqrt%283%29%2C+6.5%2C+-60%2F7%2C1-sqrt%2819%29+%29\"$
\n" ); document.write( "
\n" ); document.write( "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.
\n" ); document.write( "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.
\n" ); document.write( "
\n" ); document.write( "COMPARING:
\n" ); document.write( "The numbers to the left are smaller than (less than) the numbers to the right, so
\n" ); document.write( " $\"1-sqrt%2819%29%3C-1\"$ and $\"sqrt%283%29%3C6.5\"$ .
\n" ); document.write( "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.
\n" ); document.write( "Negative numbers are to the left of zero, so they are less than zero:
\n" ); document.write( " $\"-9%3C0\"$ , $\"-60%2F7%3C0\"$ , $\"1-sqrt%2819%29%3C0\"$ , $\"-1%3C0\"$ .
\n" ); document.write( "Positive numbers are to the right of zero, so they are less than zero:
\n" ); document.write( " $\"2%3E0\"$ , $\"sqrt%283%29%3E0\"$ , $\"6.5%3E0\"$ , $\"8%3E0\"$ .
\n" ); document.write( "
\n" ); document.write( "ABSOLUTE VALUE:
\n" ); document.write( "Negative numbers are to the left of zero, positive numbers are to the right of zero.
\n" ); document.write( "The absolute value of a number is the distance between the number and zero in the graph, and It is always a positive number.
\n" ); document.write( "For example,
\n" ); document.write( " $\"-1\"$ with $\"abs%28-1%29=1\"$ is $\"1\"$ unit to the left of zero.
\n" ); document.write( " $\"-60%2F7\"$ with $\"abs%28-60%2F7%29=60%2F7\"$ is $\"60%2F7=8%261%2F7\"$ units to the left of zero.
\n" ); document.write( "
\n" ); document.write( "PRACTICAL TIPS:
\n" ); document.write( "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.
\n" ); document.write( " $\"-60%2F7\"$ = -8.571428571428571428571428571428....
\n" ); document.write( "so you can use $\"-60%2F7=-8.6\"$ (rounded) to figure out where to plot that value.
\n" ); document.write( "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.
\n" ); document.write( " $\"1-sqrt%2819%29=-3.36\"$ (rounded)
\n" ); document.write( "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.
\n" ); document.write( "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
\n" ); document.write( " $\"-3%261%2F3\"$ = -3.333333333... and plot $\"1-sqrt%2819%29\"$ = approximately $\"-3.36\"$ $\"1%2F3\"$ of a unit to the left of $\"-3\"$ . \n" ); document.write( "

\n" );