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Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 decade ago

can anyone explain the difference between irrational and rational numbers to me?

in a way i can understand and easily comprehend

10 Answers

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  • MsMath
    Lv 7
    1 decade ago
    Favorite Answer

    rational numbers can be expressed as a fraction.

    .8 is rational because it can be written as 4/5

    sqrt(2) is irrational because it cannot be written as a fraction p/q

    If a number is rational, then it is NOT irrational.

    A real number must be either rational or irrational but not both.

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  • Anonymous
    1 decade ago

    Rational Numbers 5/1, 1/2, 1.75, -97/3 ...

    A rational number is any number that can be written as a ratio of two integers (hence the name!). In other words, a number is rational if we can write it as a fraction where the numerator and denominator are both integers.

    The term "rational" comes from the word "ratio," because the rational numbers are the ones that can be written in the ratio form p/q where p and q are integers. Irrational, then, just means all the numbers that aren't rational.

    Every integer is a rational number, since each integer n can be written in the form n/1. For example 5 = 5/1 and thus 5 is a rational number. However, numbers like 1/2, 45454737/2424242, and -3/7 are also rational, since they are fractions whose numerator and denominator are integers.

    So the set of all rational numbers will contain the numbers 4/5, -8, 1.75 (which is 7/4), -97/3, and so on.

    Is .999 repeating a rational number? Well, a number is rational if it can be written as A/B (A over B): .3 = 3/10 and .55555..... = 5/9, so these are both rational numbers. Now look at .99999999..... which is equal to 9/9 = 1. We have just written down 1 and .9999999 in the form A/B where A and B are both 9, so 1 and .9999999 are both rational numbers. In fact all repeating decimals like .575757575757... , all integers like 46, and all finite decimals like .472 are rational.

    --------------------------------------------------------------------------------

    Rational Numbers 5/1, 1/2, 1.75, -97/3 ...

    A rational number is any number that can be written as a ratio of two integers (hence the name!). In other words, a number is rational if we can write it as a fraction where the numerator and denominator are both integers.

    The term "rational" comes from the word "ratio," because the rational numbers are the ones that can be written in the ratio form p/q where p and q are integers. Irrational, then, just means all the numbers that aren't rational.

    Every integer is a rational number, since each integer n can be written in the form n/1. For example 5 = 5/1 and thus 5 is a rational number. However, numbers like 1/2, 45454737/2424242, and -3/7 are also rational, since they are fractions whose numerator and denominator are integers.

    So the set of all rational numbers will contain the numbers 4/5, -8, 1.75 (which is 7/4), -97/3, and so on.

    Is .999 repeating a rational number? Well, a number is rational if it can be written as A/B (A over B): .3 = 3/10 and .55555..... = 5/9, so these are both rational numbers. Now look at .99999999..... which is equal to 9/9 = 1. We have just written down 1 and .9999999 in the form A/B where A and B are both 9, so 1 and .9999999 are both rational numbers. In fact all repeating decimals like .575757575757... , all integers like 46, and all finite decimals like .472 are rational.

    --------------------------------------------------------------------------------Irrational Numbers sqrt(2), pi, e, the Golden Ratio ...

    Irrational numbers are numbers that can be written as decimals but not as fractions.

    An irrational number is any real number that is not rational. By real number we mean, loosely, a number that we can conceive of in this world, one with no square roots of negative numbers (such a number is called complex.)

    A real number is a number that is somewhere on a number line, so any number on a number line that isn't a rational number is irrational. The square root of 2 is an irrational number because it can't be written as a ratio of two integers.

    Other irrational numbers include the square root of 3, the square root of 5, pi, e, and the golden ratio. (For more information about pi and e, see Pi = 3.14159... and E = 2.71828..., also from the Dr. Math FAQ.)

    Pi is an irrational number because it cannot be expressed as a ratio (fraction) of two integers: it has no exact decimal equivalent, although 3.1415926 is good enough for many applications. The square root of 2 is another irrational number that cannot be written as a fraction.

    In mathematics, a name can be used with a very precise meaning that may have little to do with the meaning of the English word. ("Irrational" numbers are NOT numbers that can't argue logically!)

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  • bubsir
    Lv 4
    1 decade ago

    If we imagine the number system as being built up from scratch we would start with counting numbers 1,2,3,... we can then use + and - to find that 4 - 5 = -1 a negative number and 4 - 4 = 0 so we get integers ... -3,-2,-1,0,1,2,3,... Then we start in with X and ÷ to get 20 ÷ 5 = 4 and then 22 ÷ 5 = 4.4 = 22/5 fractions and decimals.

    Using these rules (X or * and / or ÷) with integers we get the "rational" numbers, a step up from integers. But it turns out that if we ask questions such as what is "a" when a X a = 2, there are no rational numbers that do the job. We believe (mathematicians believe) that this number must exist. If it isn't rational, it must be "not rational" or irrational. It can sometimes be difficult to show whether a number is or is not irrational.

    It turns out the questions about "squares" and square roots or even cube roots and higher are not the end of numbers to be found. pi (π) the famous ratio of the circumference to the radius of a circle is not the solution to any kind of square, cube, fourth power etc. question. It is irrational but also considered transcendental!!

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  • 1 decade ago

    Rational numbers are those that can be written as fractions involving whole numbers: for example, 3/2, 5/17, -23/947. It turns out that the decimal expansions of rational numbers will always cycle eventually. So, for example,

    1/7=.142857 142857 142857.....

    Irrational numbers are those that are not rational. In other words, they cannot be written as a fraction involving whole numbers. An example is sqrt(2). A different characterization is that their decimal expansions do not cycle. For example,

    .101001000100001...

    where the number of 0's increases by one between each 1, will be an irrational number.

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  • ?
    Lv 6
    1 decade ago

    Yeah - I teach math.

    A rational number can be expressed as a fraction, meaning that it can be converted to a ratio of a numerator and a denominator.

    An irrational number is one that is NOT an integer and has a decimal portion that does NOT repeat AND does NOT terminate (end).

    Understand that a decimal that DOES repeat can still be expressed as a fraction, and therefore is rational. Example is one third, or 1/3, which is 0.33-repeating. Don't confuse this with Pi, which is 3.14 rounded but which actually NEVER ends and NEVER repeats its decimal string of digits - so Pi is irrational.

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  • 1 decade ago

    A rational number can be written as a fraction, like 1/3. If a number is irrational, it cannot be written as a/b for any a,b. Sqrt(2) is irrational, so it is not equal to any fraction.

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  • 1 decade ago

    Don't trust me completly on this:

    A rational number is a number that has an end, when a number is irrational, it can go on forever like with pi or the square root of 2.

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  • 1 decade ago

    omg,im just learning this and just asked some questions!

    i htink i get it now!

    altough some ppl answered with very long answers,thats good but can be really confusin!!!!!!!!!!!!!!!!!!!

    so easily put:

    irrational numbers are like this

    3.1453682292202004376493067016763764728916487

    and everything else is rational:

    3.44444444

    1.4

    3

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  • 1 decade ago

    Rational numbers: I, II,III,IV,V,IX, X, L, C, M.......

    I/IV, V/IC......

    Irational numbers: π = ΧΧΙΙ / VII only approximate

    Irational = It doesn't express as a "ratio"

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