varsha16
contestada

Express the following in p/q form, where p and q are integers and q is not equal to 0.

(i) 1.272727..... (ii) 0.1282828.......


pls give the answer with steps

thank you!!!​

Respuesta :

boatengalbert291
(I)1.272727... = 14/11
(II)0.1282828...= 127/990

(The solution is in the picture
NB : the two points on the two numbers in the solution means those two numbers are recurring or repeating )
Ver imagen boatengalbert291
XxVenomousWisdomxX

[tex]\huge{\purple{\underline{\underline{\red{\mathfrak{\bigstar answer:: \bigstar}}}}}}[/tex]

(i) 1.272727...

[tex]\rightarrowtail[/tex] [tex]\boxed{\blue{\bf{1.\overline{27}}}}[/tex] [tex]\bf{i.}[/tex]

[tex]\rightarrowtail[/tex] [tex]\boxed{\blue{\bf{Let\:x\:be\:1.\overline{27}}}}[/tex]

Multiplying both the sides by 100.

[tex]\rightarrowtail[/tex] [tex]\boxed{\blue{\bf{x\:*\:100=1.\overline{27}\:*\:100}}}[/tex]

[tex]\rightarrowtail[/tex] [tex]\boxed{\blue{\bf{100x=127.\overline{27}}}}[/tex] [tex]\bf{ii.}[/tex]

Subtracting [tex]\bf{i.}[/tex] from [tex]\bf{ii.}[/tex]

[tex]\rightarrowtail[/tex] [tex]\boxed{\blue{\bf{100x\:-\:x=127.\overline{27}\:-\:1.\overline{27}}}}[/tex]

[tex]\rightarrowtail[/tex] [tex]\boxed{\blue{\bf{99x=126}}}[/tex]

[tex]\rightarrowtail[/tex] [tex]\boxed{\green{\bf{x=\dfrac{126}{99}}}}[/tex]

Reducing it to lowest form

[tex]\rightarrowtail[/tex] [tex]\boxed{\green{\bf{x=\dfrac{14}{11}}}}[/tex]

[tex]\gray{\rule{300pt}{0.3em}}[/tex]

(ii) 0.1282828...

[tex]\rightarrowtail[/tex] [tex]\boxed{\blue{\bf{0.1\overline{28}}}}[/tex]

[tex]\rightarrowtail[/tex] [tex]\boxed{\blue{\bf{Let\:x\:be\:0.1\overline{28}}}}[/tex]

Multiplying both sides by 10

[tex]\rightarrowtail[/tex] [tex]\boxed{\blue{\bf{x\:*\:10=0.1\overline{28}\:*\:10}}}[/tex]

[tex]\rightarrowtail[/tex] [tex]\boxed{\blue{\bf{10x=1.\overline{28}}}}[/tex] [tex]\bf{i.}[/tex]

Multiplying both sides by 100

[tex]\rightarrowtail[/tex] [tex]\boxed{\blue{\bf{10x\:*\:100=1.\overline{28}\:*\:100}}}[/tex]

[tex]\rightarrowtail[/tex] [tex]\boxed{\blue{\bf{1000x=128.\overline{28}}}}[/tex] [tex]\bf{ii.}[/tex]

Subtracting [tex]\bf{i.}[/tex] from [tex]\bf{ii.}[/tex]

[tex]\rightarrowtail[/tex] [tex]\boxed{\blue{\bf{1000x\:-\:10x=128.\overline{28}\:-\:1.\overline{28}}}}[/tex]

[tex]\rightarrowtail[/tex] [tex]\boxed{\blue{\bf{990x=127}}}[/tex]

[tex]\rightarrowtail[/tex] [tex]\boxed{\green{\bf{x=\dfrac{127}{990}}}}[/tex]

[tex]\gray{\rule{300pt}{0.3em}}[/tex]

Hope it helps..♪