Question

if the number is 1/2 +2 / 3 + 3/ 4 + 4 /5 Express the the decimal terminating​

Answer 1

Explanation:

To find: 1/2+2/3+3/4+4/5 is expressed as a decimal, will it be terminating or non-terminating

We know that for a fraction to terminate its denominator prime factorization should be in the form of 2^m*5^n

Let us analyse each fractions separately whether it is terminating or non terminating.

First, 1/2 ; => 2 = 2^1*5^0 its denominator is in the required form (2^m*5^n). Thus, it will have a terminating decimal expansion.

Second , 2 / 3 ;=> 3 its denominator is not in the form of 2^m*5^n

Thus, it will have a non terminating decimal expansion

Third, 3/4; => 4 its denominator is in the form of 2^m*5^n

Thus, it will have a terminating decimal expansion.

fourth, 4/5; => 5 its denominator is in the form of 2^m*5^n

Thus, it will terminate in decimal expansion

In total the sum of all the fractions will not give a terminating decimal expansion, since 2/3 doesn't give a terminating decimal expansion.