Note \(\sqrt{negative numbers}\) or \(\frac{number}{0-zero}\) are NOT real !!

On the GRE by default, any number mentioned in the quant section is a real number so must NOT assume that it is an integer unless stated clearly.


1) The Number Line


A real number line, or simply number line, allows us to visually display real numbers by associating them with unique points on a line. The real number associated with a point is called a coordinate. A point on the real number line that is associated with a coordinate is called its graph. To construct a number line, draw a horizontal line with arrows on both ends to indicate that it continues without bound. Next, choose any point to represent the number zero; this point is called the origin.

The scale need not always be one unit. Each tick mark might represent a unit fraction.







The opposite of any real number a is \(−a\). Opposite real numbers are the same distance from the origin on a number line, but their graphs lie on opposite sides of the origin and the numbers have opposite signs.

The opposite of a negative number is positive: \(−(−a) = a\).


2) Identify the Place Value of a Digit

The place value of a digit is simply the different value that each place has in a number.





3) Absolute Value


The absolute value of a real number a, denoted |a|, is defined as the distance between zero (the origin) and the graph of that real number on the number line. Since it is a distance, it is always positive.

\(|-4|=4\) and \(|4|=4\)





Also, it is worth noting that \(|0|=0\)


Think of a real number whose distance to the origin is 5 units. There are two solutions: the distance to the right of the origin and the distance to the left of the origin, namely, {±5}. The symbol (±) is read “plus or minus” and indicates that there are two answers, one positive and one negative.

\(|-5|=5\) and |\(5|=5\)

See more here: Absolute Numbers