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Practically every application of numbers for ordinary every day real life is a real number (versus imaginary or complex numbers).

Counting numbers (1,2,3,...) are natural numbers. If you use zero, then you have whole numbers. Negative numbers (used in temperature, altitude, banking, and others). Now you have the integers. Speaking of banking, with dollars and cents, you now have rational numbers (pennies are 1/100 cent). Other fractions (rational) are in use as well.

Irrational Numbers can be used to calculate materials needed (say you want as square with 10 square feet area, to find the perimeter: one side is square root of 10 (irrational number) then multiply by 4, to find the amount needed for all four sides. A real person would round this to whatever precision is convenient. Another commonly used irrational number is pi (rounded off to 3.1416 or so) which is used to find the area and circumference of circles.

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Related Questions

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