Yes, 6.333... is a rational number because it can be expressed as a fraction of two integers. In this case, 6.333... can be written as 19/3, which is a ratio of two integers. Therefore, 6.333... is a rational number.
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Well, honey, a rational number is any number that can be expressed as a fraction, where the numerator and denominator are both integers. So, if you can write 6.333 as a fraction, then it's rational. Spoiler alert: 6.333 is just 19/3 in disguise, so yeah, it's a rational number.
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It must be a generalised rational number. Otherwise, if you select a rational number to multiply, then you will only prove it for that number.
Yes. Any rational number divided by another rational number is also rational.