# What is the condition for the decimal expansion of a rational number to terminate? Explain with the help of an example.

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What is the condition for the decimal expansion of a rational number to terminate? Explain with the help of an example.

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Solution: Let x = p/q be a rational number, such that the prime factorization of q is of the form 2m5n, where n, m are non-negative integers. Then x has a decimal expansion which terminates.

Example:

Since the denominator is of the form 2m x 5n, the rational number has a terminating decimal expansion.