Decimal Expansion

DecimalExpansion

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Decimalexpansion

Pirnot (2014)assert that a decimal expansion of a number denotes its illustrationin base -10 in the decimal structure. For example, the decimalexpansion of π is 3.14159…, while that of 1/3 is 0.33333…Rational numbers have either repeating decimals i.e. a number whosedecimal illustration ultimately becomes episodic, for example, 1/3 =0.3333… = 0.3 or determinate decimal expansions i.e. even numberssuch as ½ = 0.5. On the other hand, irrational numbers do not haveterminate or periodic decimal expansions, for example, π denoted as3.14159…. As such, decimal expansions of irrational numbers arecontinually infinite and do not repeat.

One cannot writean irrational number as a simple fraction, but it can appear as adecimal as irrational numbers have infinite non-repeating numerals tothe right of a decimal point. For example, π is an irrational numbersince one cannot express it in terms of a simple fraction or ratio,only in terms of a decimal. Another example is the square root of 2or 3 i.e. √2 = 1.414213..,√3 = 1.732050..,

Pirnot (2014)defines integers as a set of number usually whole numbers that do notinclude decimal or fractional part, for example, -1, -4, 0, 1, 5,212, etc. On the other hand, whole numbers refer to numbers such as1, 0, 2, 3, etc. thus, integers differ from whole numbers as theyinclude negative numbers. Natural numbers refer to counting numbersi.e. whole numbers without zero or whole numbers hence, includenumbers such as 1, 2, 3, 0, etc. depending on the theme. The mostcommon and simplest way to use integers, irrational numbers, andwhole numbers is to count, for example, six friends, $2000, or tocount number of buildings in a street, etc. One can add numbers tomake a set of new numbers or place a space to show differences, finddistances, or work out calculations.

References

Pirnot, T. L. (2014). Mathematicsall around (5th ed.). Boston, MA:Pearson Education.