Question

The decimal expansion of 49/2³5³
contains six digits after the decimal point.


true ya false and justify the question​

Answer 1

SOLUTION

TO CHECK

TRUE / FALSE below statement

The decimal expansion of 49/2³5³ contains six digits after the decimal point.

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

$\displaystyle \sf{ \frac{49}{ {2}^{3} \times {5}^{3} } }$

Since denominator contains only 2 and 5 as factor

So the given number is terminating

Now max{3,3} = 3

The fraction terminates after 3 terms

Hence the given statement The decimal expansion of 49/2³5³ contains six digits after the decimal point. Is FALSE

FINAL ANSWER

The given statement is FALSE

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2. without actually performing the long division state whether 13/3125 and 13/343 will have a terminating decimal expansion...

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Answer 2

The answer is False.....

Thank you...

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