Question

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!!!​

Answer 1

(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 )

Answer 2

`\huge{\purple{\underline{\underline{\red{\mathfrak{\bigstar answer:: \bigstar}}}}}}`

(i) 1.272727...

`\rightarrowtail`
`\boxed{\blue{\bf{1.\overline{27}}}}`
`\bf{i.}`

`\rightarrowtail`
`\boxed{\blue{\bf{Let\:x\:be\:1.\overline{27}}}}`

Multiplying both the sides by 100.

`\rightarrowtail`
`\boxed{\blue{\bf{x\:*\:100=1.\overline{27}\:*\:100}}}`

`\rightarrowtail`
`\boxed{\blue{\bf{100x=127.\overline{27}}}}`
`\bf{ii.}`

Subtracting
`\bf{i.}` from
`\bf{ii.}`

`\rightarrowtail`
`\boxed{\blue{\bf{100x\:-\:x=127.\overline{27}\:-\:1.\overline{27}}}}`

`\rightarrowtail`
`\boxed{\blue{\bf{99x=126}}}`

`\rightarrowtail`
`\boxed{\green{\bf{x=(126)/(99)}}}`

Reducing it to lowest form

`\rightarrowtail`
`\boxed{\green{\bf{x=(14)/(11)}}}`

`\gray{\rule{300pt}{0.3em}}`

(ii) 0.1282828...

`\rightarrowtail`
`\boxed{\blue{\bf{0.1\overline{28}}}}`

`\rightarrowtail`
`\boxed{\blue{\bf{Let\:x\:be\:0.1\overline{28}}}}`

Multiplying both sides by 10

`\rightarrowtail`
`\boxed{\blue{\bf{x\:*\:10=0.1\overline{28}\:*\:10}}}`

`\rightarrowtail`
`\boxed{\blue{\bf{10x=1.\overline{28}}}}`
`\bf{i.}`

Multiplying both sides by 100

`\rightarrowtail`
`\boxed{\blue{\bf{10x\:*\:100=1.\overline{28}\:*\:100}}}`

`\rightarrowtail`
`\boxed{\blue{\bf{1000x=128.\overline{28}}}}`
`\bf{ii.}`

Subtracting
`\bf{i.}` from
`\bf{ii.}`

`\rightarrowtail`
`\boxed{\blue{\bf{1000x\:-\:10x=128.\overline{28}\:-\:1.\overline{28}}}}`

`\rightarrowtail`
`\boxed{\blue{\bf{990x=127}}}`

`\rightarrowtail`
`\boxed{\green{\bf{x=(127)/(990)}}}`

`\gray{\rule{300pt}{0.3em}}`

Hope it helps..♪