Whats the difference between irrational and rational numbers?

Question

it was a question on my math homework:
the real number line consists of rational and irrational numbers. explain the difference between these two types of numbers.

Find four numbers between 5 and 7 (two must be rational and two irrational) use word and/or numbers to explain why the are rational or irrational.

Answer 1

A number is rational if and only if it can written as a ratio of integers, otherwise it is irrational.

Here are two rational numbers between 5 and 7:
6 and 6.5.
(6 can be written as 6/1 and 6.5 as 13/2.)

That's easy. I'll give you one irrational. You'll need to think of one more.
square root of 47 = 6.855654...

Answer 2

Is 1 2 Rational Or Irrational

Answer 3

A rational number can be expressed in the form a/b where a and b are integers. So, 1/2 and 3/1 (=3) are rational. An irrational number cannot be expressed in the form a/b where a and b are integers. So, PI and the square root of 2 are irrational. The discovery that the square root of 2 is irrational was of great concern to the Pythagoreans.

Answer 4

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RE:
Whats the difference between irrational and rational numbers?
it was a question on my math homework:
the real number line consists of rational and irrational numbers. explain the difference between these two types of numbers.

Find four numbers between 5 and 7 (two must be rational and two irrational) use word and/or numbers to explain why the are...

Answer 5

rational numbers are numbers that you can express exactly as a ratio of two integers. If the are irrational then you can't do this.
Example 1/2 is obviously the ratio 1 to 2 so its rational. Pi - no.

Answer 6

Four numbers between 5 and 7; 2 rational and 2 irrational:

rational: 6 and 6.25
irrational: square root of 26 and square root of 48.

There are literally hundreds of acceptable answers.

Answer 7

A rational number is a number that can be written as a ratio, or quotient, of two integers.

An irrational number is any real number that is NOT a rational number (it can't be written as a fraction in which the numerator and denominator are integers).

"Find four numbers between 5 and 7 (two must be rational and two irrational) use word and/or numbers to explain why the are rational or irrational."
5½ and 6¾ are rational numbers, because they can be expressed as "a over b" where "a" and "b" are both integers and "b" is NOT zero. (5½ = 11/2 and 6¾ = 27/4).
√28 and √32 are examples of irrational numbers, because they can not be expresed in terms of "a/b" where "a" and "b" are both integers, and b does not equal zero. (√28 = 5.2915026... and √32 = 5.6568542...).

Answer 8

rational numbers can be expressed as the ratio of 2 integers.
ex 2/5; 5/7. 2/5=.4; 5/7=0.71428571428571428571428571428571
while this string of nombers never ends, it repeates 714285 over & over again.

Irrational numbers can't be ecpressed as the ratio of 2 integers and there is no repeating sequence as there is with 5/7
ex
π=3.1415926535897932384626433832795
e=2.7182818284590452353602874713527
√3=1.7320508075688772935274463415059

Answer 9

Rational numbers are numbers that can be expressed in the form of p/q, where p and q are real numbers, and q is not equal to zero. Irrational numbers can not be expressed in this form.

5.25 is a rational number because it is equal to 21/4, and 7 is a rational number because it can be expressed as 7/1. I can't think of any irrational numbers off the top of my head that fall between 5 and 7, but I'm sure there are plenty of them.

Answer 10

A rational number canbe expressed as a/b Where b not =0. An irrational numbet does not have this property.

Rational examples are 5.5 = 11/2 and 5.75 = 23/4
Irrational numbers are sqrt(37) and sqrt (39)