Sets in Mathematics are the collection of definite objects that can form a group. The collection of numbers, days of the week, types of vehicles,...
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April 11, 2024Decimals in Maths: Initially, when numbers were started being used for calculation, it was being used for very basic calculations, but when trade increased, and nations grew, there was a need to count large units of currency and goods which is why decimals came to exist. Decimal fractions are said to be developed by China in the 4th Century BC, and then they spread to the Middle East and from there to Europe. The Decimal Number System is denoted by a decimal point, consisting of a whole number part and a fractional part separated by a decimal point. The dot in a Decimal number is called a Decimal Point, and the Decimals are referred to as the digits after the Decimal Points.
The Decimal Number System is one of the essential number systems in Mathematics. Students learn Decimals at an early age in order to solve mathematical problems within fractions of seconds. You can check NCERT Solutions for Class 6 Maths Chapter 8 for a better understanding of Decimals. We have provided detailed information on Decimals in this article. Read on to find out about its definition, properties, types, conversions and examples.
Decimals represent the integers and non integers numbers. It is denoted by a dot present between whole numbers and fraction part called a decimal point. For example, 12.5 where 12 is whole number, 5 is fractional part and the dot (.) is denoted as decimal point.
Decimals fractions were first developed by Chinese in the 4th century BC. And it is used in our day to day life by representing money, length, mass, weight etc. We all know that all the decimal can be represented as fractions.
For example,
The properties of Decimal are as follows:
There are three types of Decimals as mentioned below:
Apart from integers, you can add, subtract, multiply and divide decimal numbers. They are as follows:
Lets us check the conversion of decimals to fractions or fractions to decimals as given below:
Decimals as fractions: Decimal points represent the tenths, hundredths, thousandths etc.
For example, 0.25 can be expanded to write as 25 x 1/100 to get 25/100.
Fractions as Decimals: We can get decimals by dividing the numerator by denominator.
For example, 3/5 = 0.6
Some of the examples of decimals are mentioned below:
Example 1: Write each of the following as decimals : (a) Two ones and five-tenths (b) Thirty and one-tenth
Solution: (a) Two ones and five-tenths = 2 + 5/10 = 2.5
(b) Thirty and one-tenth = 30 + 1/10 = 30.1
Example 2: Write each of the following as decimals: (a) Seven-tenths (b) Two tens and nine-tenths (c) Fourteen point six (d) One hundred and two ones (e) Six hundred point eight?
Solution:
(a) Seven-tenths= 7 /10 = 0.7
(b) Two tens and nine-tenths = (2 × 10) + (9 × 1 /10 ) = 20 + 0.9 = 20.9
(c) Fourteen point six = 14.6
(d) One hundred and two ones = (1 × 100) + (2 × 1) = 100 + 2 = 102
(e) Six hundred point eight = 600.8
Example 3: Write the following decimals as fractions. Reduce the fractions to lowest form. (a) 0.6 (b) 2.5 (c) 3.8
Solution: Given, a) 0.6 (b) 2.5 (c) 3.8
a) 0.6 = 6 /10 = 3/5
Hence, 0.6 = 3 /5
b) 2.5 = 2 + 0.5
= 2 + 1/ 2 = 5/ 2
Hence, 2.5 = 5/ 2
c) 3.8 = 3 + 8/10
= 3 + 4/ 5 = 19/ 5
Hence, 3.8 = 19/ 5
The frequently asked questions about Decimals are given below:
Q. What are decimals? A. These are the numbers that consist of whole number part and fractional part separated by a decimal point. |
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Q. What are the types of decimal? A. Recurring decimal, Non-Recurring decimal and Decimal Fraction. |
Q. How to convert fractions to decimal? A. To convert fractions to decimal, you can divide the numerator by denominator. |
Now you are provided with detailed information on decimals in this article. We hope this detailed article helps you. If you have any doubt regarding Decimals, you can drop your comments below. We will get back to you at the earliest.