Yes, the set of rational numbers is closed under addition.
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Yes. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.
Yes. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.
Yes. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.
5.01001000100001... is not a rational number. Rational numbers will always repeat when written in a digital form. Since it is not rational, it cannot be written as a fraction with integer numerator and denominator.
Fractions where both the numerator and divisor are rational numbers are always rational numbers.