Question

write whether the rational number 7 by 75 will have a terminating decimal expansion or and and non terminating repeating decimal expansion

Answer 1

Hey there!!

Thanks for ur Question ,

We know that , terminating decimal ,means that a fraction which decimal form is upto limited place it can be repeated or non repeat


whereas , Non terminating repeating Decimal whose decimal forms is repeated and doesn't end

ok now coming to the Question
here we have denominator 75
we know if denominator satisfy
${2}^{m} \times {5}^{n}$
then it will be Terminating decimal where , m and n = power

so ,
$\frac{7}{75} \\ = > \frac{7}{ {3}^{1} \times {5}^{2} }$
since the no is not in form of
${2}^{m} \times {5}^{n}$
therefore it is non terminating repeating decimal



Hope this helps u !!

Answer 2

here is your answer .......

hope this would help you.....

all the best for your board exams....