Question

Is it possible for a fraction to have a decimal equivalent that does not repeat and does not terminate? Explain. WILL FAN AND MEDAL!

Answer 1

1/7 = 0.1428571428547...

This number has a decimal value which repeats
(the 142857 is the repeating pattern),
and it doesn't terminate, it goes on and on forever.

This what we call a `rational number`.
When you see that word "rational" think of "ratio".
A rational number is a fraction of whole number or integers.

Other rational numbers: 1/4, 2/5, 7/2.
If top and bottom are both integers, you have a rational number,
even when the decimal does not terminate.

Answer 2

So, It can be equivalent?

Answer 3

There are these nasty numbers called `non-rationals`.
\(\large\rm \pi\), \(\large\rm \sqrt{2}\), \(\large\rm \sqrt{3}\)

These values will give us decimals which will not terminate,
but will also not have a repeating pattern.

So these are the kinds of things the question is asking about.

Answer 4

So here is an example of a fraction \(\large\rm \dfrac{\pi}{2}\)
which has a decimal equivalent that does not terminate,
and does not repeat a pattern.

Answer 5

? so it can be equivelant? or is it a yes-no kind of thing?

Answer 6

zepdrix pardon for my intervention but i think that does not terminate so than this is necessary pepeating bc. after these 9 digits from zero till 9 so there will be necessary repeating one

or not ?

Answer 7

@zepdrix please

Answer 8

@phi your opinion about this please ? ty.

Answer 9

I gave you an example of a fraction \(\large\rm \dfrac{\pi}{2}\)
which has a non-terminating decimal,
with no repeating pattern.

So that answers the original question: Yes.

Answer 10

Ok, thx.

Answer 11

@jhonyy9 I think the word repeating means that, at some point, the entire pattern of numbers will repeat.

Sure, you'll run into little repeats here and there throughout the decimal values of pi. But you'll never see the entire decimal pattern repeat.

Answer 12

I think the question is assuming the fractions are using rational numbers
i.e. pi/2 is cheating.

so they (probably) expect you to say no

Answer 13

what mean this non terminating decimal ? not that guess till infinity ?

Answer 14

Ya sorry Thadds, I'm not sure what level of math you've covered. Maybe your teacher is just being lazy with the wording of this question.

Answer 15

-_-. He will exept this.

Answer 16

accept*

oh ok :)