Quantitative Aptitude > Decimals

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Decimals

   

  • The decimal number system is based on representing numbers using powers of 10. The place value of each digit corresponds to a power of 10. For e.g. the digits of the number 7,532.418 have the following place values.

That is,

   

  • If there are a finite number of digits to the right of the decimal point, converting a decimal to an equivalent fraction with integers in the numerator and denominator is a straightforward process. Since each place value is a power of 10, every decimal can be converted to an integer divided by a power of 10. For example,

  • Conversely, every fraction with integers in the numerator and denominator can be converted to an equivalent decimal by dividing the numerator by the denominator using long division. The decimal that results from the long division will either terminate, as in  and , or the decimal will repeat without end, as in  One way to indicate the repeating part of  a decimal that repeats without end is to use a bar over the digits that repeat.  Here are some examples of fractions converted to decimals.

  • Every fraction with integers in the numerator and denominator is equivalent to a decimal that terminates or repeats. That is, every rational number can be expressed as a terminating or repeating decimal. The converse is also true; that is, every  terminating or repeating decimal represents a rational number.
  • Not all decimals are terminating or repeating; for instance, the decimal that is equivalent to  is 1.41421356237…, and it can be shown that this decimal does not terminate or repeat. Since such decimals do not terminate or repeat, they are not rational numbers and are called irrational numbers.

 

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