Decimals are the short way to express fractions and mixed numbers having denominators with power 10, like 10, 100, 1000, 10000, etc. If a number is given with a decimal point, then the first digit to the right of the decimal point indicates the number of tenths, the second digit to the right of the decimal point indicates the number of hundredths, the third digit to the right of the decimal point indicates the number of thousandths, and so on.
For example, if we take a number like 532.125, it can be expressed in the following ways:
If we start from the left-hand side, 5 hundred, 3 tens, 1 once, 0.1 tenths, 0.02 hundredths, and 5 thousandths place.
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How to Convert Decimal to Binary?
The decimal number system uses any of the 10 digits (0 to 9) to represent a number. So it has a base of 10. The binary number system represents a number using only two digits, 0 and 1. Therefore this number system is said to have a base of 2. A decimal number can be represented as an equivalent binary number. When a decimal number is converted to an equivalent binary number, the base of the number changes from 10 to 2. This is how decimal to binary conversion takes place.
- The commonly used method for converting a decimal number into a binary number is by 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 a decimal number to a binary number, the integer part of a given decimal number is divided by 2 repeatedly.
- The remainder in each step is noted down till 0 is obtained as the final quotient.
- These remainders, when written in reverse order, give the binary value of the integer part of the given decimal number.
- For conversion of a decimal part of the number to an equivalent binary value, multiply it by 2.
- Note down the value of the integer part of the product, which will be either 0 or 1. Continue multiplying the remaining decimal part and note the integer part of the result of every step till we get 0.
- Then write the noted integer values serially, which will be the equivalent binary number of the given decimal part.
Type of Decimals
- Terminating Or Recurring Decimal numbers:
The terminating or recurring decimal numbers are the sequence of numbers that repeats themselves. For example, 0.777777 is a terminating or recurring decimal number as the number after the decimal i.e.7 is repeating. It can also be written as 0.7.
- Non-terminating or Non – Recurring Decimal numbers:
Non-terminating decimal numbers are numbers that are not repeated after the decimal point.
For example, 234.6574 is a non-terminating decimal number because the numbers after decimals are not repeated. The non-terminating decimal numbers are called irrational numbers because they cannot be written in fraction form.