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More About Numbers

First a quick refresher about numbers. These are the ones you should already know about. Examples include...

Natural Numbers: 1, 2, 5, 18, 150, 1,586, 258,569.
Whole Numbers: 0, 1, 2, 5, 18, 150, 1,586, 258,569.
Integers: -258,589, -1,586, -150, -18, -5, -2, -1, 0, 1, 2, 5, 18, 150, 1,586, 258,569.
Even Numbers: -18, -6, 2, 8, 256
Odd Numbers: -55, -47, -5, 3, 453, 1,536,859
Rational Numbers: 16/5 = 3 1/5 = 3.2
Prime Numbers: 2, 3, 5, 7, 11, 13, 17, 19.
Composite Numbers: 4 (2*2), 6 (2*3), 8 (4*2), 15 (3*5), 33 (11*3)
Opposite Numbers: -2 and 2, -589 and 589, -4,587 and 4,587.

Absolute value

An absolute value is a type of number that is a measure of amount. Basically, you strip the positive and negative sign from the number and what you have left is the absolute value. In reality, it is a measure of distance from the zero. -4 is four notches away from the zero on the number line. That means the absolute value of -4 is 4. We also use a special symbol to represent absolute value. They are two vertical lines on the sides of the number.

Examples: |-4| is 4, |58| is 58.

Pi

Pi is a special value. Pi is the quotient of a circumference of a circle and its diameter as a fraction. This is kind of moving into geometry, but it's an awesome number that is used everywhere. Everywhere. It is an irrational number that is a decimal that never ends. Here is the start of pi....

3.1415926535897932384626433832795028841971693993751058209749
445923078164062862089986280348253421170679821480865132823066
470938446095505822317253594081284811174502841027019385211055
596446229489549303819644288109756659334461284756482337867831
652712019091456485669234603486104543266482133936072602491412
737245870066063155881748815209209628292540917153643678925903
600113305305488204665213841469519415116
and so on. Forever.

If you need to remember anything, remember that pi is about 3.14. That will get you pretty far. If you're looking for a very close rational number (NOT equal to pi), it's about 22/7.

Irrational numbers

Irrational numbers are numbers that are not finite. 2 is a finite number. -6 is a finite number. Even 3/4 is a finite number since you can make a decimal .75. Finite numbers do not run on forever. An irrational number can run on forever. We just talked about Pi's value of 3.1415926535897... It just runs on forever without ending. Pi is a great example of an irrational number.

Remember that a rational number is one that can be made with a ratio or fraction. Even 137/65 is a rational number (although a weird one). There is no fraction in the universe that equals Pi. Another good example is √2.You know that the square root of 4 is 2. The square root of 2 is an irrational number at 1.41421... There is no fraction in the universe that can equal that value either. There is no rational number in the world that can equal that value. The decimals will never repeat and never end.

Examples: √2, Π, √3, √7

Real numbers

Real numbers are the set of all numbers we have learned about up to this point. Every number that is a rational or irrational number is a real number. Prime numbers are real numbers. Pi, e, those crazy roots... They are all real numbers.

Examples: Every number on a number line. Every one.

Figurate Numbers

We like the idea of figurate numbers. They're not really useful, but we enjoy seeing the patterns in these numbers. Figurate numbers are based on geometric patterns. Imagine the shape of a square. It is made of one box. One is the first number in the series. If you want to keep the same square shape and divide the box with two lines, you get four boxes. Four is the second number. If you divide the box with two lines (thirds) you get nine boxes and the number nine. It works like that.

Examples: 1,4,9,16 (square shape). 1,3,5,9 (triangle shape).

You may see other patterns emerging in these numbers, but we'll save that for later.

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