Question

The decimal expansion of
156÷150
will terminate after how many places of decimal?

Answer 1

Answer:

the decimal expansion terminate after 2 place

Answer 2

SOLUTION

TO DETERMINE

After how many decimal places the decimal expansion of

$\displaystyle \sf{ \frac{156}{ 150 } }$

will terminate

CONCEPT TO BE IMPLEMENTED

Let us consider a fraction $\displaystyle \sf{ \frac{p}{q} }$

If q can be written as

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

Then the fraction is said to be terminating and terminates after r terms

where r = max{m, n}

EVALUATION

Here the given number is

$\displaystyle \sf{ \frac{156}{ 150 } }$

$\displaystyle \sf{ = \frac{52}{ 50 } }$

Now denominator = 50

$50 = {2}^{1} \times {5}^{2}$

Since denominator contains only 2 and 5 as factor

So the given number is terminating

Now max{1,2} = 2

The fraction terminates after 2 terms

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