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.
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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.
Given : 2.312
ANSWER :
2.312 is terminating ,so it is a RATIONAL NUMBER.
2.312 = 2312/1000 = 17² × 2³/ 5³×2³ = 289/125
2.312 =289/125
Hence, 2.312 is a RATIONAL NUMBER.
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Hi ,
2.312 is a rational number .
Since it is a terminating decimal.
2.312
= 2312/1000
= ( 2³ × 289 )/( 2³ × 5³ )
= 289/5³
= p/q
Denominator q , is of the form 2^n5^m,
where ,
n = 0 and m = 3
I hope this helps you.
: )
2.312 is a rational number .
Since it is a terminating decimal.
2.312
= 2312/1000
= ( 2³ × 289 )/( 2³ × 5³ )
= 289/5³
= p/q
Denominator q , is of the form 2^n5^m,
where ,
n = 0 and m = 3
I hope this helps you.
: )
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