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Q: May the sum of a rational and an irrational number only be a rational number?

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It may be a rational or an irrational number.

The sum of two irrational numbers may be rational, or irrational.

The answer depends on the fraction. If it is a ratio of two integers then the rational number is the fraction itself. If the numerator or denominator of the fraction is irrational then the fraction may be irrational and so may not have a rational number.

Decimals are real. They can be rational or irrational.

No. And in general, if a number has a finite number of decimal digits, it is rational.If it has an infinite number of digits, it may be rational or irrational.

ANY number with a finite number of decimal digits is RATIONAL.(Also, numbers with an infinite number of decimals may be rational - in which case the digits repeat - or irrational.)

Let your sum be a + b = c, where "a" is irrational, "b" is rational, and "c" may be either (that's what we want to find out). In this case, c - b = a. If we assume that c is rational, you would have: a rational number minus a rational number is an irrational number, which can't be true (both addition and subtraction are closed in the set of rational numbers). Therefore, we have a contradiction with the assumption that "c" (the sum in the original equation) is rational.

rational. Just remember that a rational number is one that may be formed from a ratio. e.g. -108/2.

Every irrational number is NOT a rational number. For example, sqrt(2) is irrational but not rational. A natural number is a counting number or a whole number, such as 1, 2, 3, etc. A rational number is one that can be expressed as a ratio of two whole numbers, which may be positive or negative. So, -2 is a rational number but not a counting number (it is an integer, though). Also, 2/3 is a rational number but not a whole, counting number or a natural number.

The product of two irrational numbers may be rational or irrational. For example, sqrt(2) is irrational, and sqrt(2)*sqrt(2) = 2, a rational number. On the other hand, (2^(1/4)) * (2^(1/4)) = 2^(1/2) = sqrt(2), so here two irrational numbers multiply to give an irrational number.

-- Any decimal that ends is a rational number. -- Any decimal that never ends may or may not be a rational number. -- The decimal representation of an irrational number never ends.

An irrational number is any number which cannot be expressed as a fraction. The number in the question can be expressed as a fraction (61,849,875,234,920,006/100,000,000,000,000) and so is rational. That being said, I suspect what has been entered was copied from a calculator, and actually represents a rounding of the number to the nearest rational number, so the answer may actually be irrational.

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