If the number $\frac{1}{2} + \frac{2}{3} + \frac{3}{4} + \frac{4}{5}$ is expressed as a decimal, will it be terminating or no-terminating?Justify your answer.

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Solution

$\frac{1}{2}$ , $\frac{3}{4}$ and $\frac{4}{5}$ have denominator of the form $2^{n} 2^{m}$ where $n$ , $m$ are non negative integers.
So, they have terminating decimal.
but $\frac{2}{3}$ do not has denominator of the form $2^{n} 2^{m}$ where $n$ , $m$ are non negative integers,
so it has non terminating decimal
Therefore sum of these cfractions has non terminating decimal

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If the number 12+23+34+45 is expressed as a decimal, will it be terminating or no-terminating?Justify your answer.

12,34 and 45 have denominator of the form 2n2m where n,m are non negative integers.So, they have terminating decimal.but 23 do not has denominator of the form 2n2m where n,m are non negative integers, so it has non terminating decimalTherefore sum of these cfractions has non terminating decimal

If the number $\frac{1}{2} + \frac{2}{3} + \frac{3}{4} + \frac{4}{5}$ is expressed as a decimal, will it be terminating or no-terminating?Justify your answer.