how to find rational and irrational numbers

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From Encyclopedia

Numbers, Rational Numbers, Rational

A number in the form of a ratio a /b, where a and b are integers , and b is not equal to 0, is called a rational number. The rational numbers are a subset of the real numbers, and every rational number can be expressed as a fraction or as a decimal form that either terminates or repeats. Conversely, every decimal expansion that either terminates or repeats represents a rational number. Rational numbers can be written in several different forms using equivalent fractions. For example, . There are an infinite number of ways to write 1, ¼ or by multiplying both the numerator and denominator by the same nonzero integer. Therefore, there are an infinite number of ways to write every rational number in terms of its equivalent fraction. The following example shows how to find the ratio of integers that represents a repeating decimal. One way to compare two rational numbers is to convert them into a decimal form. Dividing the numerator by the denominator results in the decimal equivalent. If the division has no remainder, then the decimal is called a terminating decimal. For example, ½ = 0.5, , and . Although some decimals do not terminate, they do repeat because at some point a digit, or group of digits, repeats in a regular fashion. Examples of repeating decimals are ⅓ = 0.333…,, and . A bar written over the digits or group of digits that repeat shows that the decimal is repeating: , and . Rational numbers satisfy the following properties. see also Integers; Numbers, Irrational; Numbers, Real; Numbers, Whole. Rafiq Ladhani Amdahl, Kenn, and Jim Loats. Algebra Unplugged. Broomfield, CO: Clearwater Publishing Co., 1995. Miller, Charles D., Vern E. Heeren, and E. John Hornsby, Jr. Mathematical Ideas, 9th ed. Boston: Addison-Wesley, 2001.

From Yahoo Answers

Question:Hi, Is there a standard way (any algorithm) to find a rational number between two irrational numbers say square_root(6) and square_root(7) ?

Answers:Square the numbers, in this case obtaining 6 and 7 Since the difference is only 1, multiply by 100, obtaining 600 and 700. Find a square in between. 600 < 625 < 700 6.00 < 6.25 < 7.00 6 < 2.5 < 7 An alternate method is to extract the square roots, average the results, and truncate the average: . 2.6457513110645905905016157536393 +2.4494897427831780981972840747059 . 5.0952410538477686886988998283452/2 = . 2.5476205269238843443494499141726 Now you have a whole plethora of rational numbers between 6 and 7

Question:I have test tomorrow and need help. i knw that irrational cannot be a fraction and rational is just the opposite.

Answers:Rationals -can be expressed as a fraction -can be expressed as a repeating decimal -can be expressed as a "terminating" decimal - square roots of perfect square rationals are rational ....e.g sqrt (4/9) = 2/3, sqrt (25) = 5, etc. a rational added to (subtraced from) a rational is a rational a rational multiplied (or divided) by a rastional is a rational (except divifding by zero) Irrationals -cannot be expressed as a fraction -cannot be expressed as a repeating decimal -cannot be expressed as a "terminating" decimal -can be expressed as a non-repeating decomal pattern e.g 0.1211211121111211111211...(Note tthe "1's" between "2's) ........3.1213141516171819202122232425... -include the square roots of rationals that are not perfect squares -include the cube roots of ationals that are not perfect cubes .............. -pi is irrational Hope this helps you


Answers:k / pi

Question:I have to find a rational and an irrational number Between two given numbers Find (a) a rational, and (b) an irrational, number between the given pair. #1) 0.3725 and 0.3726 a) I picked 0.37255 is that ok b)? #2) 3 and a)? b)? Thank you so much!

Answers:1 a. Yes, 0.37255 = 37255/100000 is rational b. How about 0.3725 + pi/1000000? This must be irrational, or else pi would have to be rational 2. a. 3.1 b) (3+pi)/2. Again, this must be irrational since pi is.

From Youtube

How to prove the sum of an Irrational and Rational number is Irrational :Watch in HD: In this tutorial, I demonstrate and explain how to prove that the sum of an irrational and a rational number is itself Irrational. To do this, I use the technique of proof by contradiction.

How to prove there are 2 Irrational Numbers such that their product is Rational :Watch in HD: In this tutorial I demonstrate how to prove that there are 2 irrational numbers such that their product is rational.