4.15 is a rational number because it can be expressed in the form of a/b where b is not equal to 0.
e.g. 4.15 = 415/100 which is in the form of a/b.
4.15 can be written in many ways: 415/100 or 83/20 or 830/200 or 415000/100000 or 4150/1000 etc. but each fraction is in the form of a/b.
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8.3 and 8.26 are both rational numbers. Their sum is 16.56. That's also a rational number. Their difference is 0.04. That's also a rational number. Their product is 68.558. That's also a rational number. Their quotient is close to 0.9952. It can't be completely written as a decimal, but it's equivalent to 413/415 and it's a rational number too.
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Yes.
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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.