Conversions of a Decimal Into Vulgar Fraction

In the mathematics, the figures can be categorized into various types such as natural number, real number, rational number, and whole number. Indeed, decimal numbers are one of them. The point in between the practitioner part and the whole number is known as decimal point. This article examines in detail regarding conversion of a decimal into a fraction. It also examines the various properties, types, and value representations of decimal integers. 

Discussion

Theoretical Concept of Fractions and Decimals

The relation between decimal and fraction is vital to comprehend to build a strong basis in mathematics. When a figure is expressed in the form of a/b, where a and b are related to whole numbers and b is not equivalent to 0, it is called fraction and the “conversion of a decimal into a fraction” can be expressed when it can get converted in the form of a decimal by either transforming the denominator to the power 10 or by using extended division method. If the denominator has numerical values such as 10, 100, 200, simply move the decimal to the numerator along with the numbers of zeroes to left. For example, 8/100 can be written as 00.8. 

Relation between decimals and fractions

Another good example for representing a relationship between decimal and fraction can be the division of pizza. Consider a crust pizza having 6 slices. Half of the pizza has been consumed that represents 3 slices in a fractional form, it can be written in the form ½, while in the decimal form it is written as 0.5.

Here, another illustration can be assumed. A person divides his garden in 8 equal parts. He grows flowers of distinct colours in each part of the garden. Among the 8 slots, he planted red flowers in 6 equal portions of the garden. 1 portion of the garden is for yellow flowers and 1 for orange flowers. The following portions provided to the flowers can be expressed in decimal and fractions which are red flowers grown in the 6/8 part of the garden representing 0.75 part. Yellow flowers grown in the ⅛ part of the garden represent 0.125 part and orange flowers grown in ⅛ part of the garden represent 0.125 part of the garden. 

What is a vulgar fraction?

A common fraction or vulgar fraction is a fractional number written in the usual way where one integer is placed above another integer divided by a line. Some common examples of vulgar fractions are 3/5, 8/9, 4/6. In the arithmetic, vulgar fraction is a part of the various equal portion of unity or whole unity. The value which denotes how many portions of the unit have to get divided is known as denominator of fraction; the value that denotes how many portions have to be taken is known as the numerator of fraction. 

Converting mixed recurring decimals to vulgar fractions

When the question is “conversion of decimal into fraction”, one has to determine whether it is converting mixed recurring decimal into a fraction or not. The following steps illustrated below show conversion of recurring decimals towards fractions.

• The first step is to input decimal forms by the way of eliminating bar from above and make it equivalent to x.
• The next step is identifying numbers of integers that have no specific bar after specific point of decimal.
• Assume there is an n-integer without bar then multiplies both of the sides by nth integer, 10nth, so that repeating decimal integer is particularly on the right side of the point of decimal.
• Next step is to write the repeated digits twice.
• Assume the bar is having n-digits; multiply both of the sides by 10n.
• Now do the division of both sides of the equation by coefficient x.
• Finally, the required vulgar fraction is obtained.

Conversion of pure recurring decimals towards vulgar fractions

“Conversion of decimal into fractions” is an important study area in this context; it can be stated by converting pure recurring decimal in the form of vulgar fraction.

• First step is to remove bar from above and make it equivalent to n.
• Now write the repeated integers twice.
• Identify the numbers having bars above.
• If the repeated decimal includes 1 repetition, multiply sides with 10.
• If the repeated decimal includes 2 repetitions, multiply sides with 100.
• Now subtract the value gained in step 1 from the value of step 2.
• Finally, divide both sides of the equation by n.
• The required vulgar fraction is obtained.

Conclusion

From the above discussion, it can be concluded that both decimals and fractions are two different forms of ways to express the numbers. The fractional numbers can be expressed in the form of a/b and b is not equivalent to 0. Whereas in decimal, the fractional value part and the whole number part are united by a decimal point, for example, 0.9. The decimals and fractions both represent the connection of a portion by the whole. Integer along with non-integer figures can be represented by Decimal numbers which is a standard form. In algebra, among the various types of numbers decimal is one of them that includes the whole number along with a fractional part that is split by decimal point