Question

without performing long division,determine which of the following rational numbers has a terminating decimal expansion: 7/15,-12/140,3/80,15/220

Answer 1

Answer:

Only 3 / 80 has terminating decimal expansion.

Step-by-step explanation:

Given rational numbers 7/15 , -12/140 ,  3/80 , 15/220

To tell which has terminating decimal expession.

We know a result which states that a rational of the form p / q has terminating decimal expansion if the denominator q is in the form of $2^m5^n$ where m , n are non negative integers.

First rational = 7 / 15

Denominator = 15

prime factorization of 15 = 3 × 5

Thus it does not has terminating decimal expansion.

Second rational number = -12 / 140 = -3 / 35

Denominator = 35

prime factorization of 35 = 7 × 5

Thus, It does not has terminating decimal expansion.

Third rational number = 3 / 80

Denominator = 80

prime factorization of 80 = 2 × 2 × 2 × 2 × 5 = $2^45^1$

Thus, It has terminating decimal expansion.

Fourth Rational number = 15 / 220 = 3 / 44

Denominator = 44

prime factorization of 44 = 2 × 2 × 11

Thus, It does not has terminating decimal expansion.

Therefore, Only 3 / 80 has terminating decimal expansion.

Answer 2

Answer:

Step-by-step explanation:

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