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TYPES OF NUMBERS

TYPES OF NUMBERS. Natural Numbers: {1, 2, 3, 4, ...} This group of numbers starts at 1. It includes 1, 2, 3, 4, 5, and so on. Zero is not in this group. It has no negative numbers. There are no numbers with decimals. These are the first numbers that we learn.

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TYPES OF NUMBERS

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  1. TYPES OF NUMBERS

  2. Natural Numbers: {1, 2, 3, 4, ...} This group of numbers starts at 1. It includes 1, 2, 3, 4, 5, and so on. Zero is not in this group. It has no negative numbers. There are no numbers with decimals.

  3. These are the first numbers that we learn. • They go on forever, so we say there are an infinite number of natural numbers. • These are "Arabic" numerals. You may also be interested in Roman numerals. • These are also called positive numbers.

  4. Whole Numbers: {0, 1, 2, 3, 4, ...} Whole numbers are the numbers you use when you count. This group has all of the natural numbers in it plus the number 0. Remember, wh "O" le numbers include the O. The first 10 whole numbers, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, are called digits.

  5. Integers are all of the whole numbers and their negatives. This group has all the whole numbers in it and their opposites, or, you might say, and their negatives. They are ...-3,-2,-1,0,1,2,3,... (The three dots means you keep going in both directions.)

  6. There are alsorational numbers. Rational numbers are all the different kinds of fractions. 1/2, 3/4, -2/3, and 5 are all rational numbers. Irrational numbers are numbers which you can write as decimals but not as fractions. Pi and the square root of 2 are irrational numbers.

  7. Real numbersare all of the rational and all of the irrational numbers put together. All of the numbers you normally deal with are real numbers. Imaginary Numbers These are all based on the imaginary number i. This imaginary number is equal to the square root of negative one. Any real number times i is an imaginary number. Examples include i, 3i, -9.3i, and (pi)i.

  8. Complex Numbers A complex number is a combination of a real number and an imaginary number in the form a + bi. The real part is a, and b is called the imaginary part. Examples include 4 + 6i, 2 + (-5)i, (often written as 2 - 5i), 3.2 + 0i, and 0 + 2i.

  9. Even Numbers: {2, 4, 6, 8, ...} An even number is a number evenly divisible by two. Odd Numbers: {1, 3, 5, 7, ...} If you try to break an odd number into pairs, it will always have one left over.

  10. Prime Numbers: {2, 3, 5, 7, 11, ...} Primes are numbers with only two factors. Prime numbershave only 2 factors. You cannot break them into smaller groups. Composite numbershave more than 2 factors. They can be broken into groups.

  11. To find prime numbers, we make a list of the natural numbers, and find their factors: Number Multiplying Factors How many factors? Prime or Composite?

  12. 1. 1 x 1 1 1 Neither 2. 1 x 2 1,2 2 Prime 3. 1 x 3 1,3 2 Prime 4. 1 x 4, 2 x 2 1,2,4 3 Composite 5. 1 x 5 1,5 2 Prime 6. 1 x 6, 2 x 3 1,2,3,6 4 Composite 7. 1 x 7 1,7 2 Prime 8. 1 x 8, 2 x 4 1,2,4,8 4 Composite 9. 1 x 9, 3 x 3 1,3,9 3 Composite

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