Question

Without actual division, determine the following rational numbers show a terminating or non- terminating decimal representation?

1. 5/21

2. 11/50​

Answer 1

Answer:

We know that if the denominator of a rational number has no prime factors other than 2 or 5, then it is expressible as a terminating, otherwise it has non - terminating repeating decimal representation. Thus, we will have to check the prime factors of the denominators of each of the given rational numbers.

In \frac{13}{80}

80

13

, the denominator is 80.

We have, 80 = 2 × 2 × 2 × 2 × 5.

Thus, 80 has only 2 and 5 as prime factors.

Hence, \frac{13}{80}

80

13

must have a terminating decimal representation.

∴ Terminating decimal representation of \frac{13}{80}

80

13

= 0.1625

Answer 2

Answer:

A decimal is terminating when the denominator of a fraction can be expressed in 2^n × 5^m form

So,

1. 5/21

= 5/7×3

It's non terminating.

2. 11/50

= 11/ 5² × 2

= 11×2/5² × 2 × 2 [ numerator and denominator is multiplied by 2 ]

= 22 / 5² × 2²

= 22 / 10²

= 22/100

= 0.22

It's terminating.