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# Number System Questions and Answers

## Number System Questions

### Concept of Number System

Number System Questions is used in nearly every single subject matter in maths. It to a great extent describes the significance of this subject. Number System mostly involves additional sub-topics such as HCF & LCM, factors, factorials, cyclicity, Euler number, digital root, unit digit, and more. The conception of unit digit can be well-read by assuming out the unit digits of all the sole digits ranging from 0 – 9 when elevated to definite capacities. The numbers are widely categorized into three groups for this use.

### Important definitions for solving Number System Questions:

**Natural Numbers:**All positive integers are called natural numbers. All counting numbers from 1 to infinity are natural numbers. N = {1, 2, 3, 4, 5, 6……..∞}**Whole Numbers:**The set of numbers that includes all natural numbers and the number zero are called whole numbers. They are also called as Non-negative integers. W = { 0,1,2,3,4,5,6,7,8,…………..∞}**Integers:**All numbers that do not have the decimal places in them are called integers. Z = {∞…….-3, -2, -1, 0, 1, 2, 3………∞}**Real Numbers:**All numbers that can be represented on the number line are called real numbers.**Rational Numbers:**A rational number is defined as a number of the form a/b where ‘a’ and ‘b’ are integers and b ≠ 0. The rational numbers that are not integers will have decimal values. These values can be of two types**Irrational Numbers:**It is a number that cannot be written as a ratio.An Irrational numbers are non-terminating and non-periodic fractions.

### Rules:

- One of the key things to note while solving questions related to number systems is that the difference between the square of two consecutive values is the total of the two consecutive numbers.
- The result is always an odd number if the squares of two consecutive numbers are subtracted.
- If there is an even number in the unit place of the value given, then afterwards the times it is multiplied, it will still have the similar number in the unit place, which is:(…..1)n=(…1)
(…7)n=(….7)

(……4)n=(……..4)

- If there is an odd number at the unit place (excluding 5), multiply the value by the same until it reaches to 1 in the unit place:(……….1)n= (……….1)
(…..3)4n = (……1)

(…….7)4n = (…….1)

Where n = 1, 2, 3