The rational number room those number which deserve to be expressed together a proportion between two integers. Because that example, the fractions 1 3 and also − 1111 8 space both rational numbers. All the integers are contained in the reasonable numbers, since any kind of integer z deserve to be composed as the proportion z 1 .

numbers which can not be created as a ratio of integers are called irrational .

every decimals i beg your pardon end are rational numbers (since 8.27 deserve to be created as 827 100 .) decimals which have a repeating pattern after some allude are additionally rationals: for example,

0.0 83333333 … = 1 12 .

The collection of rational number is closed under all four simple operations: that is, given any type of two reasonable numbers, your sum, difference, product, and also quotient is additionally a reasonable number (as lengthy as us don"t divide by 0 .)

The Venn diagram below shows the relationship of the various sets that numbers.


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You are watching: A rational number is a number that can be written as a of two integers.

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