Question

which of the following have non terminating decimal expression 17/210, 23/9,17/80, 35/50​

Answer 1

SOLUTION

CORRECT QUESTION

Which of the following has a non terminating decimal expansion

A. 77/210

B. 23/8

C. 17/8

D. 35/50

CONCEPT TO BE IMPLEMENTED

$\displaystyle\sf{Fraction = \frac{Numerator}{Denominator} }$

A fraction is said to be terminating if prime factorisation of the denominator contains only prime factors 2 and 5

If the denominator is of the form

$\sf{Denominator = {2}^{m} \times {5}^{n} }$

Then the fraction terminates after N decimal places

Where N = max { m , n }

EVALUATION

CHECKING FOR OPTION : A

Here the given fraction is

$\displaystyle\sf{ \frac{77}{210} }$

$\displaystyle\sf{ = \frac{11}{30} }$

Denominator = 30

30 = 2 × 3 × 5

Since the prime factorisation of the denominator contains a factor as 3

So this fraction has non terminating decimal expansion

CHECKING FOR OPTION : B

Here the given fraction is

$\displaystyle\sf{ \frac{23}{8} }$

Denominator = 8

8 = 2 × 2 × 2

Since the prime factorisation of the denominator contains prime factor only as 2

So this fraction has terminating decimal expansion

CHECKING FOR OPTION : C

Here the given fraction is

$\displaystyle\sf{ \frac{17}{80} }$

Denominator = 80

80 = 2 × 2 × 2 × 2 × 5

Since the prime factorisation of the denominator contains prime factor only as 2 and 5

So this fraction has terminating decimal expansion

CHECKING FOR OPTION : D

Here the given fraction is

$\displaystyle\sf{ \frac{35}{50} }$

$\displaystyle\sf{ = \frac{7}{10} }$

Denominator = 10

10 = 2 × 5

Since the prime factorisation of the denominator contains prime factor only as 2 and 5

So this fraction has terminating decimal expansion

FINAL ANSWER

Hence the correct option is

$\displaystyle\sf{ A. \: \: \: \frac{77}{210} }$

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