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Raising Numbers to Various Powers | Rules of Exponents | Roots & Radicals | Signed Numbers & Roots | Rational & Irrational Numbers | Real & Imaginary Numbers | Finding Square Roots & Other Roots | Summary Rational and Irrational
Numbers
A rational number is any number that results when we divide one integer by another (except zero). Examples of rational numbers are:
An irrational number cannot be expressed as this type of a fraction. An example of an irrational number is: Most of the time we do not get a whole number when calculating square roots, cube roots, or other roots. In the numbers from one to one-hundred, for example, only ten are perfect squares, those are 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100. Most of the time when calculating square roots, your answer will not come out evenly, and you will get either rational numbers with remainders, or irrational numbers with long, unending remainders past the decimal point. So, no matter how far you carry out the answer, you will not get the exact square root. You will never get an exact value. The more places you carry out the answer, of course, the closer you will be to the true value. So you have to figure out how much accuracy you need. For the purposes of this lesson, we will carry the answers out to two places past the decimal point. Let's find the square root of 17 as an example of an irrational number: This root (4.123105626) will never come out even, or give an exact value. Although your irrational 'root' will never be an exact root, it comes closer to a true value when it is carried out to more decimal places. So what we have to do with irrational numbers is to decide how much accuracy we need. In this case, we will keep only two digits past the decimal point and still be close to the squared number. How close? Well, 4.122 = 16.9744, which is only about 15 hundredths of one percent off from the true value. So we will keep two digits past the decimal, and drop the rest. So here is the answer we would give: Please go to the links below for additional instruction for this topic included on the HSEE: Rational & Irrational
Numbers: Real and Imaginary Numbers (top) Real numbers are the ones you use every day that you can add, subtract, multiply, divide, find roots of, and raise to powers. Imaginary numbers are numbers that cannot exist by following the rules of math that we have learned. Here's an example: The square root of negative four is an imaginary number because there is no number we can multiply by itself to get a negative four. (2)(2) = 4 and (-2)(-2) also = 4. You will not be working with imaginary numbers at this point, but you should be able to recognize one when you see it. For more instruction on square roots and rational and
irrational numbers along with Practice Exercises go to: Please go to the link below for additional instruction for this topic included on the HSEE: Properties of Real Numbers:
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