A rational number is a number that deserve to be created in the form p/q wherein p and q space integers, and also q ≠ 0. The collection of rational number is denoted through Q or \(\mathbbQ\). Examples:1/4, −2/5, 0.3 (or) 3/10, −0.7(or) −7/10, 0.151515... (or) 15/99. Reasonable numbers can be stood for as decimals. The different types of rational numbers are Integers prefer -1, 0, 5, etc., fractions like 2/5, 1/3, etc., end decimals choose 0.12, 0.625, 1.325, etc., and also non-terminating decimals with repeating fads (after the decimal point) such together 0.666..., 1.151515..., etc.

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1.Decimal depiction of reasonable Numbers
2.Decimal representation of Terminating rational Number
3.Decimal depiction of Non-Terminating reasonable Number
4.Solved instances on Decimal representation of reasonable Numbers
5.Practice questions on Decimal representation of rational Numbers
6.Frequently Asked inquiries (FAQs)

Decimal depiction of rational Numbers


The decimal depiction of a reasonable number is convert a rational number right into a decimal number that has the same mathematical value as the rational number. A rational number deserve to be represented as a decimal number through the aid of the long division method. We division the given rational number in the long department form and the quotient i beg your pardon we acquire is the decimal representation of the reasonable number. A rational number have the right to have two types of decimal representations (expansions):

TerminatingNon-terminating but repeating

Note: any kind of decimal representation that is non-terminating and non-recurring, will be one irrational number. 

Let"s shot to know what room terminating and also non-terminating terms. While dividing a number through the long division method, if we get zero together the remainder, the decimal development of together a number is referred to as terminating.

Example: 1/2

Let us see the long division of 1 by 2 in the complying with image:

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1/2 = 0.5 is a end decimal

And while separating a number, if the decimal expansion continues and also the remainder does not end up being zero, that is dubbed non-terminating.

Example: 1/3

Let united state see the long department of 1 by 3 in the following image:

 

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1/3 = 0.33333... Is a recurring, non-terminating decimal. You can an alert that the number in the quotient keep repeating.


Decimal depiction of Terminating reasonable Number


The terminating decimal expansion means the the decimal depiction or expansion terminates after a certain number of digits. A reasonable number is terminating if it have the right to be to express in the form: p/(2n×5m). The reasonable number whose denominator is a number that has actually no other variable than 2 or 5, will terminate the an outcome sooner or later on after the decimal point. Think about the rational number 1/16.

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Here, the decimal expansion of 1/16 terminates after 4 digits. Right here 16 in the denominator is 16 = 24. Note that in terminating decimal expansion, girlfriend will find that the prime factorization the the denominator has actually no various other factors other 보다 2 or 5.


Decimal depiction of Non-Terminating Decimal Number


The non-terminating however repeating decimal expansion means the although the decimal representation has an infinite variety of digits, there is a recurring pattern come it. The rational number who denominator is having a factor other than 2 or 5, will certainly not have a end decimal number as the result.

For example:

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Note the in non-terminating but repeating decimal expansion, girlfriend will find that the prime factorization the the denominator has factors other than 2 or 5.

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Important Notes


If a number deserve to be express in the kind p/(2n×5m) where p ∈ Z and m,n ∈ W, then the reasonable number will certainly be a terminating decimal.Terminating decimal expansion means the the decimal representation or development terminates ~ a certain variety of digits.Every non-terminating however repeating decimal representation corresponds to a reasonable number even if the repetition starts ~ a certain number of digits.