Answer:
[tex]\frac{7}{11}[/tex]
Step-by-step explanation:
We require to have 2 equations with the repeating decimal after the decimal point
given 0.636363....
let x = 0.63 ( multiply both sides by 100 )
100x = 63.63....
subtracting the first equation from the second equation gives
99x = 63 ( divide both sides by 99 )
x = [tex]\frac{63}{99}[/tex] = [tex]\frac{7}{11}[/tex] ← in simplest form
The simplest form as a fraction that 0.63 can be written as is [tex]\mathbf{ \dfrac{7}{11}}[/tex]
A fraction denotes a part of a whole number which is composed of a numerator and denominator.
To write 0.63 as a repeating fraction in its simplest form, we have the following calculations.
Let's assume that;
To change 0.63 to fraction, we multiply both sides by 100
Now;
Then, using elimination method;
100a - a = 63.63 - 0.63
99 a = 63
[tex]\mathbf{a = \dfrac{63}{99}}[/tex]
[tex]\mathbf{a = \dfrac{7}{11}}[/tex]
In conclusion, 0.63 can be written as a fraction in its simplest form as [tex]\mathbf{ \dfrac{7}{11}}[/tex]
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