2.312,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.
Answers
QUESTION : 2.312 = 2.31212…..
ANSWER : 2.31212….. is non terminating recurring ,so it is a RATIONAL NUMBER.
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...
2.312
This number has terminating Decimal
expansion .
So we can write it as
2.312 = 2312/1000
2.312 = 1156/500
2.312 = 578/250
After simplifications we get
2.312 = 289/ 125
So , The given number is a rational
number having terminating decimal
expansion