Question

To which set of numbers does the following number belong 6.3 repeating

Answer 1

If 6.3 where 3 is repeating belongs to set of rational numbers in mathematics.

Because 3 is repeating.

So, it can written as ratio of 19 over 3

As shown below

$\frac{19}{3}$

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Answer 2

Answer:  The answer is the set of rational numbers.

Step-by-step explanation: We are given to tell that to which set of numbers 6.333 . . . belong.

We have the following set of real numbers -

(i) Rational numbers : They are of the form $\dfrac{p}{q},~~q\neq 0$, where p and q are integers. They can also be written in decimal form, such that the digits after the decimal either terminate or repeats themselves. For example

$\dfrac{5}{4}=1.25,~~~\dfrac{4}{3}=1.333~.~.~..$

(ii) Irrational numbers : Here, the digits after the decimal are non-terminating and non-repeating.

For example, √2=1.142 . . ..

Thus, 6.33 . . . is a rational number, since the digits after the decimal are repeating. Also, its fractional form is

$6.33~.~.~.=\dfrac{19}{3}.$

Hence, it is rational.