Decimals are the collection of numbers that lies between integers on a number line. It can be said that decimals are another way to represent fractions in mathematics. An integer is a number placed to the left of the decimal point and whole numbers are the numbers placed to the right of the decimal point, called decimal fractions.
In mathematics, a decimal number is denoted by a number consisting of two parts. One is a whole number part and the other is the decimal part, both separated by a given decimal point. Similarly, a decimal number has a dot and it is called a decimal point. The digits after the decimal point represent a value lesser than one. The number of digits contained in the decimal part of a decimal number denotes the decimal places.
For example, 20.654 is a decimal number in which 20 is the whole number and 654 is the decimal part. These two parts are separated by a decimal point. It has three decimal places. Again, 0.37 is also a decimal number in which the whole part is zero and the decimal part is 37. This number has two decimal places.
In the above examples, 24.65 can be considered as an expression of a mixed fraction which is a combination of a whole part and a proper fraction. The decimal number 0.37 is a proper fraction represented in decimals only. Cuemath is the best platform to learn this topic in detail.
In decimals, as we go from left to right after the given decimal point, the place value of the digits gets divided by ten, which means the decimal place value finds the tenth, hundredth, etc. Thus, the decimal form 0.3 means 3/10, and the decimal from 0.09 refers to 9/100.
Types of Decimal Numbers
Decimal Numbers can be of different kinds. These are as follows:
Recurring Decimal Numbers (Repeating decimal digits)
Example: 2.135135
Non-Recurring Decimal Numbers (Non Repeating decimal digits)
Example: 5.16328
Like Decimal Numbers (Decimals having the same decimal places)
Example: 7.05. 8.32, 21.49 are like decimals as all of them have two decimal places.
Unlike Decimal Numbers (Decimals having different decimal places)
Example: 2.6, 9.04, 35.883 are unlike decimals.
Conversion of Decimals to Binary
All number systems are known to consist of a base that represents the total no. of digits that are used in that number system. The decimal number system has 10 as a base because it uses 10 digits to represent a number that is 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Similarly, the binary number is the number system with a base of 2 because in this number system, any number is represented by two digits, and those are 0 and 1.
A decimal number can be represented as a binary number. When the number is converted from decimal to binary, the base of the number changes from ten to two. All decimal numbers have their equivalent binary numbers. The commonly used method for converting a decimal number into a binary number is performing short division by 2 with the remainder (for integer part) and performing short multiplication by 2 with the result (for the decimal part).
To convert decimal to binary, the integer part of a given decimal number gets divided many times by 2. The remainders are written till we get 0 as the final quotient. Then these remainders are written in reverse order to get the binary value of the integer part of the given decimal number.
For conversion of a decimal part to binary, multiply it by 2. jot down the value of the integer part of the product, which will be either 0 or 1. Continue multiplying the remaining decimal part till we get 0 and note the integer part of the result of every step. Then write the noted integer results serially, which will be the equivalent binary number of the given decimal part.