Question

find 6/15 is a terminating or non terminating without performing actual long division . if it is a terminating find the decimal expansion of this.
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Answer 1

Note: A fraction p and q is a terminating decimal, only when prime factors of q are 2 and 5.

According to Question,

Given : (6/15)

Take the common factor '3'.

$=> \frac{2}{5}$

$=> \frac{2}{1 * 5}$

$=> \frac{2}{2^0 * 5^1}$

⇒ 0.4

Since, the denominator is expressed in the form of 2^n * 5^m, So it has a terminating decimal representation.

Hope it helps!

Answer 2

Answer:

Concept: For a fraction to be terminating, the denominator must be made up of only prime factors : 2 and 5. That is, the prime factorisation of denominator must be in terms of 2 and 5 only. It can be in powers of 2 and 5 also.

Coming to the question,

6 / 15 has a denominator 15

But the case I mentioned works only in the simplest case. That is, the fraction must be in the simple form.

So 6 / 15 can be converted to simple form by dividing by common term 3.

=> 2 / 5

Here denominator is 5, So it obeys our rule.

So it is terminating.

Now we know that division by multiples of 10 is more easier that numbers.

So 2 / 5 , can be converted to a fraction having 10 as denominator to make our calculations easier.

So Multiplying by 2 to both numerator and denominator we get,

=> 2 * 2 / 5 * 2

=> 4 / 10

=. 0.4

So the decimal expansion is 0.4 and it is a terminating decimal.