Rational and Irrational Numbers???? Can any1 help?! Pleeeeez!!?

Question

In algebra II we're learning bout rational and Irrational numbers and i can not get it at all. the teacher doesn't explain it very well can any one help and explain them to me.

Answer 1

Rational numbers are numbers which can be written as a ratio of two INTEGERS (4 is a rational number b/c it is a ratio of 8/2, 12/3, etc). Irrational numbers are numbers which cannot be written as a ratio of two integers (square root of 2 is irrational, because you can't write it as a ratio. square root of 25 though, is rational because it's equivalent to 5, which can we be written as 10/2, 15/3, etc).

Answer 2

Rational number - any number that can be represented by a fraction { a/b, b not equal to zero, a and b are in the set of integers }

Irrational numbers - non-repeating, non-terminating set of numbers - numbers like pi. Others are things like the square root of two.

If the number terminates or repeats, it could be represented as a fraction of some sort. The rational and real numbers compose the set of real numbers.

Answer 3

a rational number is any number that can be written as a fraction of integers.

for instance : 0.25 = 25/100 , thus 0.25 is a rational number.
12 = 12/1 , thus 12 is also a rational number.

now you might think that all numbers are rational numbers .

0.33333333333333333333..... = 1/3 also rational.

but the square root of 2 , can not be written as a fraction of two integers.

the number pi ( with circle ) can not be written as a fraction of two integers , so not rational bbut irrational.

Answer 4

Rational numbers are numbers that can be predicted. Decimals that repeat like .3333 is rational, whole numbers are rational like 2 or 5, and nice fractions that equal nice decimals are rational like 1/4 = .25. irrational numbers are unpredictible, you don't know which number is next. These are usually weird decimals like .5243584321841, or pi.

Answer 5

Rational numbers are numbers that can be written as the RATIO of two integers. Their decimal equivalents either terminate or repeat. Examples: 1/3, -4/5

Irrational numbers are numbers that cannot be written as the ratio of two integers. Their decimal equivalents never terminate and never repeat (although there could be a pattern, like .101001000100001...) Examples: pi, e.

Answer 6

Rational numbers can be written as fractions (ratio of 2 integers); irrational numbers cannot. there is NO FRACTION that's equal to √2.

In Alg 2 the trick is to convert repeating decimals to fractions. Say you had N = 0.151515...... Since the cycle repeats every 2 decimal places, multiply N by 100 (10 to the 2nd) and then subtract N:

100N = 15.151515......
..... N = 0.151515......
-------------------------------
99N = 15.000000000....
N = 15/99 = 5/33.

Answer 7

Remember that Integers are ...-2,-1,0,1,2,3,4.... A rational number is any number that can be written as p/q where p and q are integers.

Irrational numbers are any real number that cannot be classified as rational....

You can think of it like this....

natural numbers (1,2,3...) are all whole numbers
whole numbers (0,1,2,3,... ) are all integers
integers (...-2, -1, 0,1,2,.... ) are all rational numbers (q is 1)
rational numbers are all real numbers
therefore irrational number are all real number that are not rational.

Hope that helps.

Answer 8

355/113 will recur with a era of length under 113. The definition wins here and says that 355/113 is rational. the priority is in assuming that 355/113, which superficially imitates pi in part of its decimal illustration, does not terminate. yet another concern is interior the fact that the rationals and irrationals are disjoint instruments by ability of their definitions. i'm curious as to why you concept that 355/113 does not recur?

Answer 9

A rational number is one that can be written in the form:

a/b where a and b are integers