Answer:
a) [tex]x=\frac{4}{11}[/tex]
b) [tex]x=\frac{11}{30}[/tex]
c) [tex]x=\frac{9}{25}[/tex]
Step-by-step explanation:
(a) Given : 0.36 repeating 36
To find : What is 0.36 repeating 36 expressed as a fraction in simplest form?
Solution :
Let [tex]x=0.36363636363.....[/tex] ......(1)
Now as there are two digits repeating immediately after decimal point, we multiply above by 100 and get,
[tex]100x=36.36363636....[/tex] .....(2)
Subtract equation (1) from (2),
[tex]99x=36[/tex]
[tex]x=\frac{36}{99}[/tex]
[tex]x=\frac{4}{11}[/tex]
(b) Given : 0.36 repeating 6
To find : What is 0.36 repeating 6 expressed as a fraction in simplest form?
Solution :
Let [tex]x=0.3666666.....[/tex] ......(1)
Now as there are one digits repeating immediately after decimal point, we multiply above by 10 and get,
[tex]10x=3.6666666....[/tex] .....(2)
Subtract equation (1) from (2),
[tex]9x=3.3[/tex]
[tex]x=\frac{3.3}{9}[/tex]
[tex]x=\frac{11}{30}[/tex]
(c) Given : 0.36
To find : What is expressed 0.36 as a fraction in simplest form?
Solution :
Let [tex]x=0.36[/tex]
[tex]x=\frac{36}{100}[/tex]
[tex]x=\frac{9}{25}[/tex]
