Definition: Every rational number can be written as a fraction with whole numbers on top and bottom. Irrational numbers can't.
Working method of recognizing them: Any number that you can write down completely , on paper, using number digits without any symbols, is a rational number, whether you write it as a fraction or as a decimal.
Popular misconception: A rational number doesn't necessarily produce a decimal that ends, and a decimal that never ends is not necessarily an irrational number. Examples: 1/3, 1/7, 1/9, 1/11 are never-ending in decimal form.
Whole numbers are the positive integers and zero.
Counting numbers are the whole numbers without zero.
Integers are the whole numbers plus their negatives.
Rational numbers can be expressed as fractions, including integers, while irrational numbers cannot and have non-repeating decimals. Integers include all whole numbers and their negatives. Counting numbers start from 1 and do not include zero, while whole numbers include zero.
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