SAMPLE College Math
calculate the absolute value of -5, then it will be denoted by |-5|and is equal to 5, showing that the distance from -5 to 0 is 5 units. Some of the properties of absolute values are: | | = { ≥0 − ( ) < 0 || − | ≥ | 0= | | | * | = | | * | | Scientific Notation Sometimeswemakeuseofsomepowerof10thatmakesitconvenienttowriteaverylargenumber;this means we are making use of scientific notation. For instance, suppose we have to write the number 687657.788. We can write it as . 6. 87657788×10 5 B. Inequalities The value of different numbers can be compared by their relative position on the number line. For instance, in the given number line below,
<
islessthan andisdenotedby also say , that is isgreaterthan andliesontherightsideofthenumberline,relativetothe > position of . The mathematical representation for different expressions is given in the following table: ,whichmeans liestotheleftof onthenumberline.Wecan
= < > ≥ ≤ ≠ ≈
Interpretations is equal to is less than is greater than is greater than or equal to is less than or equal to is not equal to
Expressions
is approximately equal to The symbols <, >, ≥,≤and≠denotethesignsofinequalitiesandtheexpressionsusingthesesignsof inequalities, , , , and denotes inequalities. We can make use of set-builder < > ≥ ≤ ≠ notationfortheseinequalitiesaswell.Forinstance, meansset representsallthevalues = { | ≥2} of such that is greater than or equal to 2. This can be shown graphically on the number line as follows:
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