Question

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

Answer 1

Answer:

Step-by-step explanation:

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 ).

Answer 2

Step-by-step explanation:

ANSWER

Let x=p/q be a rational number such that the prime factorization of q is of the form 2

m

5

n

, where n, m are positive integers.

Then x has a decimal expansion which terminates.

Example:

500

49

×

2

2

×5

3

49

Since the denominator is of the form 2

m

×5

n

, the rational number has a terminating decimal expansion.

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