Question

4.57 bar is an (a) integer (b) rational number (c) natural number (d) irrational number​

Answer 1

Answer:

b) Rational number

Step-by-step explanation:

4.57 bar = 4.575757575757...

Any number that is not non-terminating and non-repetitive is an irrational number.

But since the above number is non-terminating but repeating it is rational.

It cannot be an integer or a natural number because of the decimal point.

Answer 2

4.57 bar  is a rational number

Rational numbers

• These are real numbers which can be written in the form p/q where p and q are integers and q≠0
• All real numbers which are not rational  are irrationals.  
• Rational numbers are terminating decimals or non terminating recurring decimal.
• Irrational numbers are non terminating non-recurring decimals
• Integers are rational numbers written in simplest form with denominator as 1
• Natural numbers are positive integers.

Step 1:

Assume that:

$N=4.\overline{57}$

Step 2:

Multiply both sides by 100

$100N =457.\overline{57}$

Step 3:

Subtract N from 100N  and solve for N

99N = 453

=> N = 453/99

=> N = 151/33

Hence N  4.57 bar  is a rational number

Correct option is b) rational number

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