What is the condition for the decimal expansion of a rational number to terminate?Explain with the help of example.
The condition required for a rational number to have a terminating decimal expansion is that when the number is in its simplest form then its denominator should be in the form of 2^m x 5^n ( where m and n are any whole number ).
10 / 100 = 0.1 ( In this we can find that when the fraction will be broken down into its simplest form then its denominator will be in the form of 2^m x 5^m )
9/81 = 0.11111111111……… ( 9/81 has a non terminating decimal expansion because when we shall break it into its simplest form then it won’t be in the form of 2^m x 5^n ).
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