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Classify all the following numbers as natural, whole. Integer rational, or irrational List all that apply. b. 0 |
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Answer» Answer: Natural numbers are the numbers 1 , 2 , 3 , ... or the numbers 0 , 1 , 2 , 3 , ... according to whose definition you CHOOSE. So 0 may be considered a natural number or not. Whole numbers are the numbers 0 , 1 , 2 , 3 , ... Integers INCLUDE negative numbers, but not fractions. So the integers are: 0 , 1 , − 1 , 2 , − 2 , 3 , − 3 , ... Rational numbers are any number that can be expressed as p q where p and q are integers and q ≠ 0 . So , 12.42 , − 17 3 and 0 are rational numbers. There are infinitely many rational numbers, but they do not form a continuous line. The continuous line of numbers is called the real number line. It includes all the previous numbers we have mentioned, but also numbers LIKE √ 2 , π and e , which are not rational. Some real numbers - such as √ 2 - are the roots of polynomials with integer coefficients. These are known as algebraic numbers. Irrational numbers are any real numbers that are not rational. So 0 is not an irrational number |
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