Decimal Fractions

Decimal fractions are an integral part of mathematics. Therefore the term decimal fractions is one in which the lower number called the denominator is a power of ten and hence is converted to decimal by placing a point or a decimal after numbers equal the number of zeros in the denominator.

In simpler words, decimal fractions are the way to represent the fractions in a decimal form. And this is done to make the calculations much easier while applying various operations.

What Are Fractions?

In mathematics, fractions are defined as the part of the whole where any number of equal parts are present. This fraction word is a  Latin word namely fracto meaning to break. Fractions are an important part of mathematics when we deal with things like the division of any item among a certain number of people or finding a certain number out of the total. Fractions are showcased as a number value demonstrating the part of a whole in terms of numerator and denominator.

For example 23/100- this is a fractional number where 23 is the numerator and 100 is the denominator.

What Are Decimals?

Decimals are another type of representation for numbers. It is a combination of the decimal part and the fractional parts. A decimal point is what separates the whole and the fractional part. This decimal number system is used for both integers and non-integers. 

This decimal number system could be understood by the following example:

23.4- a number is a decimal number where 23 is whole and 4 is the fractional part.

How to Convert Fractions Into Decimals?

The decimal number system and fractional number system are two different concepts but here exist the third which is the decimal fraction system. 

Decimal fractions are the number system in algebra, where a fraction is converted into decimal but the condition is the denominator part must be a power of ten. 

Moreover, this fraction with a denominator having the power of ten is converted into a decimal number system by placing a decimal point according to the rules.

The conversion begins with applying the formula “a ÷ b”, where a is the numerator and b is a denominator, and simply place the decimal point after the number of digits equal to the number of zeros in the denominator.

For example:  let us take a fractional number 23/100.

To convert this fractional number into a decimal number, the number is written as 0.23.

Here, we will apply the decimal point after two numbers because there are two zeroes in the denominator.

How To Convert A Decimal Into A Fraction?

The conversion of decimal into a fraction is the complete opposite process. To better understand the conversion process for decimal into a fraction, let us take this example.

0.0058 is the fraction we would consider, and to write this in fractional form just count the number of digits from the right side placed after the decimal point. For instance, in the above we have 4 decimal places after the point hence the zeroes in the denominator will be 4. 

Therefore in the decimal form, the number will be 58/10000.

Convert The Following Fraction Into Decimal?

The conversion from decimal to fraction and the fraction to decimal has been explained and hence below are some of the examples to take a better look at the concept.

Convert decimal into fraction

1. 0.0034

The decimal number 0.0034 will be written as 34/10000

1. 0.426

The decimal number 0.426 will be written as 426/1000

1. 1.45

For the decimal number 1.45, the fractional form will be 145/100

1. 35.686

The decimal number 35.686 will be written as 35686/1000 in the fractional form.

Moreover, if the denominator contains a number other than the power often then simply divide the numerator by the denominator and the quotient is the decimal form for it. 

For example, ⅔  is the fractional form and the decimal form for this numeric value is 1.5

Convert fraction into a decimal

1. 78/100

The decimal form for the above fractional number is 0.78.

1. 89/10

The decimal form is 8.9

1. 892/100

The decimal form for 892/100 is 8.92.

1. 5/8

0.625 is the decimal form for fraction ⅝.

Conclusion

Hence the concept of the decimal fraction system is a very useful one in mathematics which simplifies the calculations at times and makes the process much simpler and easy. It all depends on the person whether to use the decimal form or the fractional form for calculations or convert one into another form as per the situation.