Examples of decimal numbers

Author: ARAS

 

The number system is called the decimal number system if it has a base value of 10, which has the most important in scientific and technological development. This is the weighted (or positional) number, which is determined by the position (or weight) of each digit in a number. The decimal system includes digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9, and it is also known as the base-10 system. The position of each digit is the power of 10, which is considered as the weight of the digit. Each position is ten times higher than the previous position in the decimal system. It signifies that the numerical value of a decimal number can be evaluated by multiplying each digit by the position in which the digit is placed and then adding the products of all pairs. Let’s understand decimal numbers with examples.

Examples of decimal numbers

We can interpret any decimal number by using the following method. Suppose we have a decimal number 1234.

\(1234 = 1 \times 10^3 + 2 \times 10^2 + 3 \times 10^1 + 4 \times 10^0\)

\(= 1000 + 200 + 30 + 4\)

\(= 1234\)

The right-sided digits are least significant, and the left-sided digits are more significant because power increases by one for every next digit from left to right to left.

Let’s interpret a floating number in decimal number system. Assume a number 1234.56.

\(1234.56 = 1 \times 10^3 + 2 \times 10^2 + 3 \times 10^1 + 4 \times 10^0 + 5 \times10^{-1} + 6 \times 10^{-2}\)

\(= 1000 + 200 + 30 + 4 + 0.5 + 0.06\)

\(= 1234.56\)

Here, the most important bit is 1 and the least significant bit is 6.

The main benefits of the decimal number system are that it is easy to read, manipulate, and are used by humans widely. There are, however, certain disadvantages, such as waste of time and space. Since the digital and hardware systems are based on binary systems (0 and 1), we need four-bit of space for each decimal number. On the other hand, Hexadecimal numbers also need 4 bit, and Hexadecimal numbers have a higher number of digits than Decimal numbers, which is an advantage of the Hexadecimal.

After matching the whole decimal string, we get the ASCII text, which is the string “Hello World”. You can convert any decimal into ASCII by following the same process.