Number System
NUMBER SYSTEM
About Human beings:
🌾Human beings have came across several number systems,
-
- Tally marks
- Hindu – Arabic number system $\{0, 1, 2, 3, 4,….\}$
- Roman number system $\{I, II, III, IV,…. \}$
- Greek number system $\{\alpha,\;\beta,\;\gamma…\}$
- Chinese number system
- Egyptian number system, etc.,
🌾Among these number systems, the world agreed and adapted to use Hindu-Arabic number system in our day-to-day life, (i.e.) for all arithmetic operations like counting, addition, subtraction, multiplication, etc., Â
🌾Hence we can simply say, human beings can understand Hindu-Arabic number system.Â
Hindu-Arabic or Decimal Number System:
Why Hindu-Arabic number system is also called as Decimal number system???
🌾How many distinct symbols are there in Hindu-Arabic number system? $$\begin{matrix} 1 & 2 & 3&4&5 \\ 6&7&8&9&10\\11&12&13&14&15\\…&…&…&…&…\\51&52&53&54&55\\…&…&…&…&…\\96&97&98&99&100\\…&…&…&…&…\\\end{matrix}$$
There are ten distinct symbols in Hindu-Arabic number system. Right???
$$\{ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}$$
These ten distinct symbols serve as the base for Hindu-Arabic number system. (i.e.) to make up any bigger number, we have to use these $10$ symbols only.
Hence, In digital world, this number system is named as DECIMAL (ten = deca) or BASE-$10$ number system.
🌾Decimal number system,
- has $10$ distinct symbols $\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}$.
- These $10$ symbols serve as a base for decimal number system.
- Hence the base value for this number system is $10$
- Humans use this number system in their day-to-day life.
How a decimal number is represented?
Place value of a decimal number:
🌾Let us consider a decimal number $879$
In $879$, we have to know the place value of $8$, $7$ and $9$. In simple words, $9$ is in ones $(10^0=1)$ place, $7$ is in tens $(10^1=10)$ place and $8$ is in hundreds $(10^2=100)$ place.
Hence$$879\;=\;8\;hundreds+7\;tens+ 9\;ones$$$$879=8×100+7×10+9×1$$$$879=8×10^{2}+7×10^{1}+9×10^0$$
🌾Let us consider a decimal number $0.175$
$$0.175=1×10^{-1}+7×10^{-2}+5×10^{-3}$$ $$=1×0.1+7×0.01+5×0.001$$
🌾Let us consider a decimal number $465.234$
$$465.234=4×10^2+6×10^1+5×10^0+2×10^{-1}+3×10^{-2}+4×10^{-3}$$ $$=4×100+6×10+5×1+2×0.1+3×0.01+4×0.001$$