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Classify the real number by choosing all the classifications that apply.

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1 Answer

Hy Kyndell,

Just to clarify, is this question asking to classify the number 3400? If so, here is how one goes about the problem:

The first categorization of a number is real or imaginary. Real numbers do not contain the number i (which represents the square root of -1). 3400 is a real number. Real numbers are numbers we would come across in real life, whereas imaginary numbers are solely intended to help solve higher-level mathematics problems.

The next categorization within real numbers is rational or irrational. Rational numbers are numbers that can be expressed as a fraction. Irrational numbers contain non-repeating, non-terminating decimals (examples include pi, e, and the square root of 3). 3400 is a rational number (as a fraction, it can be expressed as 3400/1).

Within rational numbers, a more specific category is integers. Integers are numbers that can be written without using fractions or decimals. Note that this includes negative numbers. 3400 is an integer.

Going one step further, whole numbers are integers excluding negative numbers. In other words, it is whole numbers beginning with 0 and moving up on the number line (0, 1, 2, 3, ...). 3400 is a whole number.

Finally, there is a final category within whole numbers called natural (or counting) numbers. This includes all whole numbers except 0 (i.e. 1, 2, 3, ...). 3400 is a natural number.

To summarize: 3400 is a real number, a rational number, an integer, a whole number, and a natural (or counting) number. Please let me know if any of this is unclear or if you have a question.