Question

3.456789123,Given real number is expressed in decimal form. Find whether they are rational or not. If rational, express them in the form p/q. Comment on factors of q.

Answer 1

ANSWER : The given number is a RATIONAL NUMBER because it is non terminating recurring

SOLUTION IS IN THE ATTACHMENT..

REAL NUMBERS :

a number which is either rational or irrational is called a real number.

RATIONAL NUMBERS :

A number that can be expressed as p/q , where p,q are Integers and q≠0 is called a rational number.

IRRATIONAL NUMBERS :

A number that cannot be expressed as p/q , where p,q are Integers and q≠0 is called a irrational number.

NON TERMINATING REPEATING DECIMAL EXPANSION :

The number which does not terminate but repeat the particular number again and again in the process of division , is said to be a non terminating repeating decimal expansion.

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

Hi ,

3.456789123 is a rational number.

Since it is a terminating decimal.

Now ,

3.456789123

= 3456789123/1000000000

= 3456789123/10^9

= 3456789123/( 2 × 5 )^9

= 3456789123/( 2^9 × 5^9 )

= p/q

denominator q is of the form 2^n × 5^m

where ,

n = 9 and m = 9

I hope this helps you.

: )