Question

write the following in decimal form and say what kind terminating or non terminating of decimal expression each has: 36 / 128​

Answer 1

SOLUTION

TO DETERMINE

The decimal form and say what kind terminating or non terminating of decimal expansion each has

$\displaystyle\sf{ \frac{36}{128} }$

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

Here the given fraction is

$\displaystyle\sf{ \frac{36}{128} }$

Expressing in decimal form we get

$\displaystyle\sf{ \frac{36}{128} = 0.28125}$

Now the given fraction can be rewritten as

$\displaystyle\sf{ \frac{36}{128} = \frac{9}{32} }$

So the denominator = 32

32 = 2 × 2 × 2 × 2 × 2

Since the prime factorisation of the denominator contains only prime factors 2

So the given fraction has terminating decimal expansion

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