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Decimal fractions are currently an integral part of mathematics. China was the first to utilise decimal fractions towards the end of the 4th century BC, and even the Middle East followed, eventually making their way to Europe via the Mediterranean. Decimal fractions paved the way for modern mathematics and statistics.
Discussion
Definition of Decimal Fractions
In mathematics, especially in algebra, a decimal fraction is a proportion in which the denominator equals ten or a multiple of 10 such as 100, 1000, 10,000, or any other number more than 10. When fractions have a decimal point but no denominator, adding, subtracting, dividing, and multiplying fractions becomes much more manageable.
Types of Decimal Fractions
There are primarily two main types and two subsidiary types of decimal fractions which are as follows:
Terminal or Non-recurring Decimal: To be precise, the phrase “non-recurring” refers to things that don’t occur repeatedly; in other words, those that come to an end or don’t recur at all. The numerator divided by its denominator is the only way to transform these fractions into decimals. For instance, dividing one by four yield the answer of 0.25 if one wants to convert 1/4 into a decimal fraction.
Recurring or Non-terminating Decimal: As the name implies, recurrent refers to things that keep repeating them; therefore, these decimal fractions never cease. For instance, 0.545454…
Pure Recurring Decimals: All digits or sets of numbers after a decimal point are repeated when a decimal fraction is created. This results in a pure form of recurring decimals. For instance, 2.373737…, 0.333333… Such repeating fractions can be simply represented by writing the first two numbers after the decimal point followed by a dot (in case one number is repeated) or a bar (in case more than one number is repeated).
Mixed Recurring Decimals: In this case, one or more numbers after the decimal point do not repeat, while the rest of the digits or the set of numerals (after the decimal point) do. For instance, 1.7232323…
Properties of Decimal Fractions
The following are essential features of decimal fractions when multiplying and dividing them.
The product remains the same regardless of every sequence in which two decimal values are multiplied. The product is identical irrespective of a series in which a whole integer and a decimal value are multiplied. Decimal fractions can be multiplied by 1 to get precisely the same result. Zero is the product of a decimal fraction multiplied by zero. The quotient of a decimal number divided by another decimal number is one. The quotient of zero divided by any decimal is zero. The quotient is the decimal number if a decimal fraction is divided by 1. It is impossible to separate a decimal number from zero since zero is not reciprocal.
Functions of Decimal Fractions
Decimal functions must be written in the aligned form for subtraction and addition. The equations will be simpler to solve.
One must not regard the decimal points when multiplying decimal functions. The decimal points are then marked to the number of decimal places specified.
Examples of Decimal Fractions
- In a fraction 3/4, its decimal fraction can be calculated as follows:
3/4 = (3 × 25) / (4 × 25) = 75/100
- To convert 5/12 into its decimal fraction, there is no simpler method since this denominator 12 cannot be factorised into products of either 2 or 5 or both. So to convert this fraction into a decimal fraction, divide five by twelve, which equals 0.42, which is the same as 42/100.
Ways to find Decimal Fractions
A most common query related to decimal fractions is how to find decimal fractions?
One needs to divide the numerator by its denominator to get the decimal representation of a fraction. After placing the decimal point and adding zeros, one must put the numerator’s smaller amount in the denominator. This indicates that if a fraction’s denominator can be represented as a factorisation from either 2 or 5 or both, it can be transformed into a decimal fraction.
Conclusion
Calculations can be made simpler by using fractions. Mathematicians use decimal fractions to determine and calculate more significant sections and then reduce these into smaller portions. Using equivalent fractions later in maths, one can decrease or simplify fractions in order to make problems more manageable and easier to solve. It is also possible to convert fractions into decimal numbers, used in all monetary systems in India and worldwide. The ability to work with decimal fractions comes in handy regularly. Understanding fractions is essential, regardless of which occupations use them the most.
