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A recap on Terminating Decimals:

– To figure out whether the fraction is terminating, bring it down to its lowest form.

– Focus on the denominator – if it is of the form , the fraction is terminating, else it is not.

Keeping this in mind, let’s look at a couple of DS questions on terminating decimals.

Question 1: If , , , and are integers and and , is a terminating decimal?

Statement 1:

Statement 2:

**Solution:**

Given: , , , and are integers

**Question:** Is a terminating decimal?

or is ?

We know that powers of 2 and 5 in the denominator are acceptable for the decimal to be terminating. If there is a power of 3 in the denominator after reducing the fraction, then the decimal in non- terminating. So our question is basically whether the power of 3 in the denominator gets cancelled by the power of 3 in the numerator. If is greater than (or equal to) , after reducing the fraction to lowest terms, it will have no 3 in the denominator which will make it a terminating decimal. If is less than , even after reducing the fraction to its lowest terms, it will have some powers of 3 in the dominator which will make it a non-terminating decimal.

**Question:** Is ?

**Statement 1:**

This statement doesn’t tell us anything about the relation between and . Hence this statement alone is not sufficient.

**Statement 2:**

This statement tells us that is greater than . This means that after we reduce the fraction to its lowest form, there will be no 3 in the denominator and it will be of the form only. Hence it will be a terminating decimal. This statement alone is sufficient.

Answer **(B)**.

Now onto another DS question.

Question 2: If , is it possible to write as a terminating decimal?

Statement 1: is an integer.

Statement 2: is an integer.

**Solution:**

Given:

**Question:** Is a terminating decimal?

Again, will be a terminating decimal if it is of the form

**Statement 1:** is an integer.

(an integer)

Is a terminating decimal? We don’t know. If has 3 as a factor, will be a terminating decimal. Else it will not be. This statement alone is not sufficient.

**Statement 2:** is an integer.

(an integer)

Is a terminating decimal? We don’t know. If has 7 as a factor, will be a terminating decimal. Else it will not be. This statement alone is not sufficient.

Taking both together,

Since and are integers, will be a multiple of 6 (and thereby of 3 too) and will be a multiple of 7. So will be a terminating decimal.

Answer **(C)**.