Question

If the number 1/2+2/3+3/4+4/5 is express decimal will it terminating online terminating justify your answer




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Answer 1

Step-by-step 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^nThus, 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

We get

Thus, it will terminate in decimal

Required answer:- ✅

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.

• Hope it helps you mate:-
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