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Pure recurring decimals are the type of decimal representation where the numbers are periodic, which continues to repeat in its own values at a certain intervals. It can be represented in a number that is rational only when it is a decimal representation which is in repetition. These are the ones where finitely many digits are figured as zero.
The sequence which shows an infinitely repeating series of digits, is known as Reptend. Suppose the repetend becomes zero, then the decimal representation is also known as a terminating decimal rather than a repeating decimal. The zeros present there can be omitted and also the decimal terminates before the zeros appear. All the terminating decimal representations are written as a decimal fraction, where the fraction is written whose denominator is a power of 10. It is also written in ratio forms. Though, every number with a terminating decimal representation also trivially has a second, alternative representation as a repeating decimal whose repetend is the digit 9. This is obtained by decreasing the final non-zero digit by one and appending a repetend of 2.000 is represented as 1.999 whereas 1.485000 can also be considered as equal to 1.484999 are two examples of this.
Vulgar Fractions:
A fraction always indicates the part of a whole or any number of absolutely equal parts. A fraction describes the number of parts of a specific size that should have, for example, one-half, eight-fifths, or three-quarters.
A standard, vulgar, or simple fraction consists of a numerator which is displayed above a line and a non-zero denominator displayed below that line. Numerators or the denominators are also used in fractions which are not common fractions, including compound fractions, complex fractions, or mixed numeral fractions.
In positive common fractions, the numerator and denominator are the natural numbers. The numerator indicates the several equal parts, and the denominator indicates how many of those parts make up a unit or a whole. The denominator cannot be zero because zero parts can never make up a whole.
A vulgar fraction is a rational number written as x/y. x and y are both integers here. The denominator (y) cannot be zero as with other fractions. The term was previously used for distinguishing the types of fraction.
Common fractions can become either positive or negative,or they can also become proper or improper fractions too. Compound fractions, complex fractions, mixed numerals, and decimals are not common fractions, though they can be evaluated as fractions unless irrational.
- A unit fraction is a common fraction which is present along with the numerator of one. Unit fractions can also be expressed using the negative exponents.
- A dyadic fraction is a type of common fraction in which the denominator is a power of two. Thus the precomposed fraction characters which are formed, are mainly included in the Number Forms in blocks.
The steps for the conversion of pure recurring decimals into vulgar fractions:
(i) To convert to decimal form, just remove the top bar and write x equal to that number.
(ii) The number of digits with no bar following the decimal point must be determined.
(iii) Once you’ve eliminated all but the last n digits without bars, multiply both sides by 10n to eliminate all but the last repeating decimal digit.
(iv) The repeating digits should be written at least twice.
(v) The number of digits having a bar after the decimal point should be found out.
(vi) Suppose there are n-digits having bars, multiplying both sides by 10n.
(vii) Then subtract the number obtained in step (i) from the number obtained in step (ii).
(viii) Then dividing both sides of the equation by the coefficient of x leads to the next step.
(ix) Thus the required vulgar fraction in the lowest form can be found.
Conclusion:
Vulgar fractions are the fractions expressed by numerator and denominator, not decimal. Proper fractions are the fractions where the numerator is less than the denominator. It has a value of less than 1. Improper fraction – is a fraction in which the denominator is greater than the numerator and has a value of 1 or more than 1.
