Comparing decimals

Recurring and terminating decimals

  • A decimal number which has finite number of digits after the decimal is called Recurring decimals.
    Example: 0.35
  • A decimal where decimal representation becomes periodic or same sequence of digits keeps repeating indefinitely is called terminating decimals.
    Example: 31.213333…

Comparing decimals

  • Any two decimal numbers can be compared by comparing their whole part and decimal parts.
  • If the whole parts are equal then the tenth parts can be compared and so on.

Compare 22.3 and 22.5
As Whole parts are equal; hence we compare tenths part.
\begin{array}{l}22.3 = 22{\rm{ }} + {\rm{ }}\dfrac{3}{{10}}\\22.5{\rm{ }} = {\rm{ }}22{\rm{ }} + {\rm{ }}\dfrac{5}{{10}}\\\dfrac{3}{{10}} < \dfrac{5}{{10}}\\\therefore 22.3{\rm{ }} < {\rm{ }}22.5.\end{array}

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