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Know that there are numbers that are not rational, and approximate them by rational numbers.
Know that there are numbers that are not rational, and approximate them by rational numbers.
Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.
Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.
The breakdown
The breakdown
All numbers can be written with a decimal point. For example, you can rewrite -4 and 10 with decimal points without changing their values.
-4 = -4.0 or -4.00 or -4.000
10 = 10.0 or 10.00 or 10.000
You can expand the decimal places of a number that already has digits to the right of the decimal point.
6.7 = 6.70 or or 6.700 and so on
Each number above has a decimal expansion that ends either in zeros or in a repeating digit. Any number with a decimal expansion that ends in zero or repeating digits is a rational number.
Some numbers do not end in zero or repeating decimals. The three dots, called an ellipsis, mean that digits continue, but not in a repeating pattern.
A number with a decimal expansion that does not end in zero or a repeating decimal is an irrational number. The most famous irrational number is pi. It is 3.141592653....
The decimal expansion of pi does not end in zero or in repeating decimal, therefore, it is an irrational number. The digits go on forever without repeating.
Every real number belongs to either the set of rational numbers or to the set of irrational numbers.
Another way to think of rational numbers are any number that can be written in the form a/b where b does not equal zero (a fraction).
Natural (sometimes called counting) numbers start with 1, 2, 3...and continue. If you start counting, you start with one and continue.
Whole numbers start with zero, and then include all natural numbers.
Integers are all whole numbers and their opposites.
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