Types of Numbers – Practice Problems

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There are different types of numbers in the real number system. When you started to count things at a very early age, you learned the natural numbers. They are numbers such as 1, 2, 3, 4, 5, and so on. Then you discovered that there is a special number, zero. Natural numbers including zero are called whole numbers. Later, you learned about negative numbers such as -1, -2, -3, and so on. These numbers together with the whole numbers are united by the term 'integers.' Apart from integers there are also positive and negative fractions and decimals, either terminating or repeating. All fractions and decimals, together with integers, are rational numbers.

There are numbers that cannot be displayed as fractions, decimals, integers, and so on, such as many square roots, like √2, as well as special numbers like pi (π), or Euler's number (℮). These numbers are irrational numbers. Note that while natural numbers are integrated into whole numbers, whole numbers are integrated into integers, and integers are integrated into rational numbers. Rational numbers and irrational numbers are opposite number systems. Either a number belongs to the rational number system or to the irrational numbers. But: all numbers, rational and irrational, together, make up the real numbers.

This video will give you insight into the types of numbers with a great analogy that is easy to remember. It will also help you understand why all integers are rational numbers but not all rational numbers are integers.

Use properties of rational and irrational numbers. CCSS.MATH.CONTENT.HSN.RN.B.3

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Exercises in this Practice Problem
Explain the different types of numbers.
Place each number in the smallest possible set.
Identify which numbers don't belong to the given number type.
Assign each number to its correct number type.
Analyze the statements about the different number types.
Decide to which number type the number belongs.