How are real numbers useful?

Answer 1

Real numbers are used in everyday life. Some subsets of real numbers you are more familiar with than others.

1. Counting numbers or Natural numbers: 1,2,3,4,5.....
2. Whole numbers: Zero is added to the counting numbers. Often we ignore zero, but it plays an important part in many calculations. Often when we do calculations and then double check we are doing subtraction, hoping to get zero for the answer meaning we got the same answer both times.
3. Integers: now we add negative numbers. A negative number could mean different things. You could subtract by adding the negative of a number (computers are actually doing this). A negative number applied to money, could mean that you owe money to somebody else. In temperature, we pick the arbitrary reference point for our zero. When it gets colder than that, we call the temperature negative.
4. Rational numbers (fractions). When we divide, more often than not, there is a remainder. We can express numbers with the fractional part, rather than stating the remainder. Also, many decimal numbers (such as our money) represents rational numbers. If you have 38 cents, then you can write it as 0.38 or 38/100 dollars.
5. The rest of the real numbers that do not fall into the above categories, are Irrational Numbers. Probably the easiest example is when you take the square root of a number (which is not a perfect square). An example, if you have a square, measuring 1 foot by 1 foot, and measure across the diagonal, you will have Square root of 2 feet. An approximate value is 1.414 feet This is almost 17 inches, but not quite. If you were to try to carry the decimal out to "the end" you would never get there. This happens with rational (like 1/3 = 0.333333...) but the difference is the sequence will form a pattern and repeat. With irrational, the pattern never repeats. If you were to try to find some fraction of some large denominator, you would never find one that would be exact. Another irrational number that comes up often, is pi. Commonly used to find circumferences and areas of circles (and areas and volumes of spheres).

Answer 2

As opposed to what? We need numbers; and integers (whole numbers) are not appropriate for all purposes.

Answer 3

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