Is this number rational or irrational?Justify your answer in 1-2 sentences.
(I)6.789
(II)-1
(III)3.111111...
(IV)4.345237
(V)1.9898989898...
(VI)✓5
(VII)✓9
(VIII)22/7
(IX)2.15798230317...
(X)1.1234567891011121314...
Answers
Answer:
(I)6.789 --> Rational
(II)-1 --> Rational
(III)3.111111... --> Rational
(IV)4.345237 --> Rational
(V)1.9898989898... --> Rational
(VI)✓5 --> Irrational
(VII)✓9 --> Irrational
(VIII)22/7 --> Rational
(IX)2.15798230317... --> Rational
(X)1.1234567891011121314... --> Rational
Step-by-step explanation:
First of all let me tell you what is rational and what is irrational.
Numbers are of two types terminating or non-terminating and non-terminating numbers are of two types :-
1. Non-Terminating Repeating Numbers --> Ex :- 3.33333..., 4.25252525...
2. Non-Terminating Non-Repeating Numbers --> Ex :- 2.010010001....
Rational numbers are terminating and non-terminating repeating numbers.
Irrational Numbers are non-terminating non-repeating numbers.
(I)6.789 --> It is rational because numbers after decimal '789' is terminating.
(II)-1 --> It is also rational number because -1 = -1.0. So it is terminating number and hence it is a rational number.
(III)3.111111... --> It is rational number because it is non-terminating repeating numbers.
(IV)4.345237 --> This number is rational number because it is terminating.
(V)1.9898989898... --> It is rational number because after decimal '98' is repeating infinitely.
(VI)✓5 --> It is irrational number because its decimal expansion will never terminate and also number after decimal do not repeat.
(VII)✓9 --> ✓9 = 3.0. So it is rational number
(VIII)22/7 --> Decimal expansion of 22/7 is 3.142857142857142857..... You can see that after decimal '142857' is repeating continuously. So it is a rational number.
(IX)2.15798230317... --> It is a rational number because you have not specified whether after decimal, numbers are repeating or not.
(X)1.1234567891011121314... --> It is irrational number because this number is following a pattern so numbers after decimal will never repeat.
Step-by-step explanation:
I hate you
..plz plz mark as brainlist
.........