Question

without actually performing the long division State whether the following rational number will have a terminating decimal expansion or a non terminating repeating decimal expansion 42/35​

Answer 1

Answer:

(42/35) is terminating.

Step-by-step explanation:

We know that,

All rational numbers can be represented in the (p/q) form, where p and q are integers and q ≠ 0.

So,

Now,

If q is of the form 2^m × 5^n, where m and n are any whole numbers, then the number is terminating.

Here,

p = 42

q = 35

We know that,

35 = 7 × 5

So,

we can say that it is non terminating because they are not of the form 2^m × 5^n,

But the truth is, they are actually terminating.

(42/35) = 1.2

This is because when a rational number is represented, it should always be in the lowest form, this gives definition and value to what we learned in our smaller classes, I mean, most of us would have wondered why we represent fractions in the lowest form.

This is the reason.

Here,

p = 42 = 7 × 8

q = 35 = 7 × 5

Here,

7 is a common factor, cancelling it out we get,

(8/5)

Now, that is in the lowest form, now we can proceed further,

Here,

q = 5 = 2⁰ × 5¹

Hence,

q is of the form 2^m × 5^n, where m and n are whole numbers.

Hence,

8/5 is terminating.

So, Directly and indirectly (42/35) is terminating.

Hope it helped and believing you understood it........All the best