The Number System

Numbers are the fundamental building stones of math. Number system is a means of counting using a particular base. You can find different kinds of numbers exist, we will learn about them in short at number system.

It contains:

Capability to find the relative values of a number.

The way to use a number in various arithmetic operations such as subtraction, addition, division and multiplication

Locating the problem solving strategies

Base 2 Number System:

The base-2 number system is also referred to as binary number system. You can find only 2 binary digits within the binary number system: 0 and 1. More specifically, the usual base-2 system is actually a radix of 2.

Base 8 Number System:

Base 8 number system is also known as octal number system and uses the digits 0 to 7. It is one of the alternatives to dealing with long binary numbers. The digits employed in the 'base 8 number system' are: 0, 1, 2, 3, 4, 5, 6 and 7.

In the octal system every place is a power of eight. Let us see with the aid of example

To change (436)$_8$ to base 10

(436)$_8$ = 4 $\times$ 8$^2$ + 3 $\times$ 8$^1$ + 6 $\times$ 8$^0$

= 256 + 24 + 6

= (286)$_10$

=> (436)$_8$ = (286)$_10$

Ancient Number Systems

A number system defines some values that is employed to symbolize quantity. A number system is how a society records and communicates ideas regarding numbers. It contains a set of elements and basic operations can be carried out on numbers. The number system have been around for 1000's of years. The common system is the existing according to number 10. The number systems can be classified into 2 categories as follows:

Non Positioned Number System: In ancient times, people utilized to count on their fingers, When fingers became insufficient for counting, other parts of the body, stones, pebbles or sticks were employed to indicate the values.

Roman number system is the most frequent non positioned number system to symbolize the numbers, for instance C (for hundred) and I, X, L, V (for fifty) etc. By 300 BC, Indians had already started using symbols to symbolize 1 to 9. By AD 600, they had developed a place system and zero. Furthermore, since it was very hard to perform arithmetic operations, no logical methods are used in this system.

Positioned Number System: The very first positioned number system was created by the Babylonians. They utilized a base 60 system. Now this system used like decimal system (base 10).

Estimating and Rounding

The Estimating and Rounding number value will be identical to the original number value however it will less exact. It is an approximate value of the original number.

Rules:

If the number we are rounding is followed by number higher than or equivalent to 5, then round the number up.

If the number we are rounding is adopted by number under 5, then round number down.

Example 1:

Round the number 43 nearest ten

Solution:

Here 3 is lower than 5, so it is rounded down

43 is rounded down to near ten digit 40

Example 2:

Round the number 46 to nearest ten

Solution:

Here 6 is more than 5, so it is rounded up

46 is rounded to near ten digit 50

Example 3:

Round the number 1975 to nearest thousand

Solution:

Here it is rounded to 2000

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