Question

without actually performing the long division find if 637/7280 will have terminating or non terminating repeating decimal expansion give reason for your answer​

Answer 1

Answer:

terminating decimal expansion

Step-by-step explanation:

upon simplification 637/7280 can be brought down to its simplest form which is 7/80

since the denominator i.e. 80 has only 2 and 5 as its factors.

80 = 2⁴ x 5

Hence 637/7280 has a terminating decimal expansion

Answer 2

Answer:

The correct answer is : terminating decimal expansion

Step-by-step explanation:

To determine if the decimal expansion of 637/7280 will be terminating or non-terminating repeating, we need to examine the denominator.

637/7280 can be simplified to 7/80.

The denominator of 7/80 is 80. We can factorize 80 to find its prime factors:

80 = 2^4 * 5

Since the prime factorization of the denominator contains only 2's, 5's and does not contain any other prime factors, the decimal expansion of 637/7280 will be terminating.

When a fraction can be written in the form of p/q, where p and q are co-prime integers and the prime factorization of q contains only 2's and/or 5's, the decimal expansion of the fraction will terminate. Therefore, the decimal expansion of 637/7280 will terminate.

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