Q-a- Without actual division- determine if -28250 is terminating or non terminating decimal number-

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Standard IX

Mathematics

Irrational Numbers

Q.(a) Without...

Question

Q.(a) Without actual division, determine if $\frac{- 28}{250}$ is terminating or non terminating decimal number.

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Dear student,

$L e t u s f i r s t c h e c k t h e g e n e r a l r u l e f o r s o l v i n g s u c h q u e s t i o n s . I t s t a t e s t h a t a r a t i o n a l n u m b e r i n t h e f o r m o f a f r a c t i o n \frac{x}{y}, w h e r e x a n d y c a n n o t b e f u r t h e r d i v i d e d, i . e t h e y h a v e n o c o m m o n f a c t o r a m o n g t h e m, i . e t h e y a r e c o - p r i m e a n d t h e d e n o m i n a t o r y c a n b e e x p r e s s e d i n t h e f o r m o f 2^{n} 5^{m} w i l l h a v e a t e r m i n a t i n g d e c i m a l e x p a n s i o n . T h u s, w e f i r s t r e d u c e t h e n u m b e r . \frac{- 28}{250} c a n b e r e d u c e d b y c a n c e l l i n g w i t h t h e c o m m o n f a c t o r 2 . T h e r e s u l \tan t i s \frac{- 14}{125} . H e n c e, 14 a n d 125 c a n n o t b e f u r t h e r d i v i d e d, t h e y a r e c o - p r i m e . B U T, 14 a n d 125 c a n n o t b e e x p r e s s e d i n t h e f o r m o f 2^{n} 5^{m} . T h e r e f o r e, t h e g i v e n f r a c t i o n \frac{- 28}{250} w i l l h a v e a n o n t e r m i n a t i n g d e c i m a c a n n o t b e e x p r e s s e d i n t h e f o r m o f 2^{n} 5^{m} . T h e r e f o r e, t h e g i v e n f r a c t i o n \frac{- 28}{250} w i l l h a v e a n o n t e r m i n a t i n g d e c i m a l .$

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Q.(a) Without actual division, determine if -28250 is terminating or non terminating decimal number.

Q.(a) Without actual division, determine if $\frac{- 28}{250}$ is terminating or non terminating decimal number.