Question

5.123456789,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

Hi ,

5.123456789 is a rational number.

Since , it is a terminating decimal.

Now ,

5.123456789

= 5123456789/1000000000

= 5123456789/( 10^9 )

= 5123456789/( 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.

: )

Answer 2

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.

TERMINATING DECIMAL EXPANSION :

The number which terminates after a finite number of steps in the process of division is said to be terminating decimal expansion.

SOLUTION :

Given : 5.123456789

5.123456789

= 5123456789/1000000000

= 5123456789/( 10^9 )

= 5123456789/( 2^9 × 5^9)

5.123456789 is terminating , so it is a rational number.

Hence, 5.123456789 is a rational number.

HOPE THIS ANSWER WILL HELP YOU...