Find 9 rational numbers between 0 and 0.1

Asked by Virender | 1st Jun, 2016, 03:00: PM

Expert Answer:

G i v e n space i n t e r v a l space i s space 0 space a n d space 0.1 F r a c t i o n a l space f o r m space o f space 0.1 space i s space 1 over 10 T h u s space w e space n e e d space t o space f i n d space t h e space r a t i o n a l space n u m b e r s space b e t w e e n space 0 space a n d space 1 over 10 T h a t space i s space w e space n e e d space t o space f i n d space 9 space r a t i o n a l space n u m b e r s space b e t w e e n space 0 over 10 space a n d space 1 over 10 N o w space c o n s i d e r space t h e space f r a c t i o n space 0 over 10 N o w space m u l t i p l y space t h e space n u m e r a t o r space a n d space t h e space d e n o m i n a t o r space o f space t h e space a b o v e space f r a c t i o n space b y space 10 T h u s comma space w e space h a v e comma 0 over 10 equals 0 over 10 cross times 10 over 10 equals 0 over 100 A n d space t h e space f r a c t i o n 1 over 10 equals 1 over 10 cross times 10 over 10 equals 10 over 100 T h u s comma space w e space n e e d space t o space f i n d space r a t i o n a l space n u m b e r s space b e t w e e n space 0 over 100 space a n d space 10 over 100 T h u s comma space w e space h a v e comma 0 over 100 less than 1 over 100 less than 2 over 100 less than 3 over 100 less than 4 over 100 less than 5 over 100 less than 6 over 100 less than 7 over 100 less than 8 over 100 less than 9 over 100 less than 10 over 100 T h a t space i s comma space w e space h a v e comma 0 less than 1 over 100 less than 2 over 100 less than 3 over 100 less than 4 over 100 less than 5 over 100 less than 6 over 100 less than 7 over 100 less than 8 over 100 less than 9 over 100 less than 0.1 T h e r e f o r e space t h e space 9 space r a t i o n a l space n u m b e r s space b e t w e e n space 0 space a n d space 0.1 space a r e colon 1 over 100 comma 2 over 100 comma 3 over 100 comma 4 over 100 comma 5 over 100 comma 6 over 100 comma 7 over 100 comma 8 over 100 space a n d space 9 over 100 rightwards double arrow 0.01 comma space 0.02 comma space 0.03 comma space 0.04 comma space 0.05 comma space 0.06 comma space 0.07 comma space 0.08 space a n d space 0.09 O b s e r v e space t h e space n u m b e r space l i n e. T h e space r a t i o n a l space n u m b e r s space b e t w e e n space 0 space a n d space 0.1 space a r e colon

Answered by Vimala | 1st Jun, 2016, 04:02: PM

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