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:

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:

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.

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:

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.