To complete each portion, use the x and y values provided. x=0.63 y=0.636363 Does x have a rational number? Is y a rational number? Justify your responses. The given value x=0.63 is a rational number. The given y=0.636363 is a ration number.
here, the rational number is any number that can be expressed as p/q, where q is not equal to zero (q[tex]\neq[/tex]0).
Given x=0.63.
We can write x as [tex]\frac{63}{100}[/tex].
So, here x=[tex]\frac{63}{100}[/tex] is in the form of [tex]\frac{p}{q}[/tex].
Therefore, x=0.63 is a rational number.
Now, Given y=0.636363....
Take the y=0.636363.... as equation (1)
Multiply the equation (1) with 100.
We get 100y=63.636363....
Take 100y=63.636363... as equation (2)
Substract equation(2) and equation (1)
We get 100y-y =63.636363...-0.636363...
99y=63
y=[tex]\frac{63}{99}[/tex].
So, here y=[tex]\frac{63}{99}[/tex] is in the form of [tex]\frac{p}{q}[/tex].
Therefore, y=0.636363... is a rational number.
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