# NUMBER SYSTEM NOTES FOR COMPETITIVE EXAMS

Dear Aspirants, We have noted down some short notes on number system for the competitive exams. You all should revise below all notes before giving any exams. It will make your knowledge deeper and help in scoring good marks.

(a) 2 is the only even prime number.

(b) Number 1 is neither divisible nor prime.

(c) Two consecutive odd prime numbers are called prime pair.

(d) All natural numbers are whole, rational, integer and real.

(e) All whole numbers are rational Integer and real.

(f) All whole numbers are rational and real.

(g) All whole numbers, rational and irrational numbers are real.

(h) Whole numbers and natural numbers can never be negative.

(i) Natural (including Prime, Composite, even or odd) numbers and whole numbers are never negative.

(j) Fractions are rational.

(k) All prime number except 2 are odd.

(l) 0 is neither negative nor positive number.

(m) If a is any number then, if a divides zero, result will be zero. If 0 divides a, then result will be infinite or not defined or undetermined i.e.

$$\frac { a }{ 0 } =0\quad but\quad \frac { a }{ 0 } =\infty (infinite)$$

where a is real number.

(n) Dividing 0 by any number gives zero e.g. $$\frac { 0 }{ a } =0$$

(o) The place or position of a digit in a number is called its place value such as Place value of 2 in 5283 is 200.

(p) The real value of any digit in a certain number is called its face value. As, face value of 2 in 5283 is 2.

(q) The sum and the product of two rational rational number is always a rational numbers.

(r) The product or the sum of a rational number and irrational number is always an irrational number.

(s) π is an irrational number.

(t) There can be infinite number of rational or irrational numbers between two rational numbers or two irrational numbers.

(u) Decimal indication of an irrational number is infinite coming. $$as\quad -\sqrt { 3 } ,\sqrt { 2 }$$

(v) The square of an even and the square of an odd number is odd.

# DECIMAL

(w) The decimal representation of a rational number is either finite or infinite recurring e.g. $$=\frac { 3 }{ 4 } =0.75(finite)$$

$$\frac { 11 }{ 3 } =3.666…(infinite\quad recurring)$$

(x) If decimal number is 0, x and 0. xy are given, then they can be expressed in the form of $$\frac { p }{ q }$$

$$As,\quad 0.x\quad =\quad \frac { x }{ 10 } \quad and\quad 0.xy\quad =\quad \frac { xy }{ 100 }$$

(y) If decimal recurring numbers $$0.\overline { x } \quad and\quad o.\overline { xy } \quad are\quad given,$$

then they can be expressed in the form of $$\frac { p }{ q } \quad As\quad 0.\overline { x } =\frac { x }{ 9 } \quad and\quad o.\overline { xy } =\frac { xy }{ 99 }$$

(z) The recurring decimal numbers of type $$0.\overline { x } \quad or\quad o.\overline { xyz }$$ may be converted to rational form as $$\frac { p }{ q } \quad follows.$$

$$0.\overline { xy } =\frac { xy-x }{ 90 } \quad or\quad o.\overline { xyz } =\frac { xyz-x }{ 990 }$$

Thanks you and All the best!

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Updated: January 14, 2018 — 2:10 pm