What are the Decimal Number and Decimal Number Systems?

The number that comprises a whole number and fractional part are called the decimal number. The number is separated by a decimal point of the whole number from the fractional part. For example, 56.49 is a decimal number in which 56 is a whole number and 49 is the fractional part.

The number system consisting of decimal numbers is known as the decimal number system.

Types of different decimal numbers

• Terminating decimal numbers: The decimal numbers in which the fractional part after the decimal point is finite or countable are known as terminating decimal,for example: 2.5
• Non-terminating decimal numbers: The decimal numbers that do not terminate after the decimal point and continue to extend up to infinity are known as non-terminating decimal numbers, for example: 1.333…

What is a counting number?

The numbers that are used for counting in real-life situations are known as counting numbers. All natural numbers are counting numbers.

What is a Fraction?

A fraction represents the equal distribution of anything. For example, if we divide a circle into four equal parts, then one part will be represented as 14. The lower part known as the denominator of the fraction represents the total parts that the thing is divided into, and the upper part known as the numerator denotes one part that is to be represented. There are two types of fractions:

Proper Fraction: The fraction whose numerator is smaller as compared to the denominator is known as a proper fraction. In other words, the total fraction that is less than one is known as a proper fraction. Example: 38 is a proper fraction.

Improper Fraction: The fractions whose numerator is greater than the denominator is known as improper fraction. In other words, the fraction that is greater than one is known as an improper fraction. Example: 52 is an improper fraction. 

What is a Decimal Fraction?

A fraction that has its denominator as 10 or multiple of 10 is known as a decimal fraction. For example,  3100 is a decimal fraction. 

Steps to Convert Decimal to Fraction

The steps given below shows how to convert decimal to fraction:

• Recognize the place value of the last digit after the decimal in the given number
• With the help of it, determine the denominator of the number
• Remove the decimal point and rewrite it in the fraction form
• Then reduce the fraction into its simplest form

Let us take an example to understand it better.

Example: Convert 0.25 into a fraction.

• Identify the place value of the last digit🡪 5 is in the hundredth place
• Therefore, the denominator of the number will be 100
• In fraction form 🡪25/100
• After simplifying it into the lowest equivalent fraction, we get 1/4

Dividing a Decimal Fraction by Counting Number

Method 1: This method is similar to the method used in the general division. The division is carried out ignoring the decimal point unless the divisor completely divides the dividend. Then the decimal number is put in the quotient as the same place where it is present on the dividend. For example, 25.64 ÷ 4 = 6.41.

Method 2: In this method, we try to remove the decimal point from the numerator then carry out the general division. For example, if we have to divide 63.96 by 3, we will multiply the numerator and denominator by 100 because the position of the last digit after the decimal point is the hundredth. 

                                     63.693  X  100100  =  6369300  =  21.23.

Conclusion

Through this piece of information, we got to learn about many different topics like decimal numbers, fractions, counting numbers and conversion of decimal into fractions, and the process of division of a decimal number by a counting number. 

A decimal number is a number that comprises a whole number and a fractional part. Fraction consists of a numerator and denominator. Counting numbers are all natural numbers.