Which simplified fraction is equal to 0.53 (the 3 is repeating)
2 answers:
<h3>Answer: Choice B. 8/15</h3>
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Explanation:
x = 0.53333333... the 3's go on forever
10x = 5.3333333..... we have infinitely many 3's here as well
100x = 53.333333..... same story
Each time we multiply both sides by 10, we move the decimal point over 1 spot to the right.
Focus on this system of equations
Note how the decimal points line up so we can see both right sides have the same 33333... pattern
If we subtract those equations straight down, the left hand side turns into 90x because 100x-10x = 90x
The right hand side terms subtract to 48. The infinite number of 3's after the decimal will cancel out when we subtract. So we basically have 53-5 = 48.
After those subtractions, we now have the new equation 90x = 48
Divide both sides by 90 and reduce
90x = 48
90x/90 = 48/90
x = 48/90
x = (6*8)/(6*15)
x = 8/15
8/15 = 0.53333333....
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There is no restrictions for x for f(x) =3✓x because you can take the cube root of any real numbers. Therefore, the domain is infinity she. dealing with the set of real numbers.
You can't take the square root of negative numbers. So, x values are restricted for f(x) = ✓x for real numbers and the domain is (0, infinity).
<h3>How to explain the domain?</h3>It should be noted that since x cannot take negative values in the question, the square root he undefined. Hence it is an imaginary value.
Also, You can't take the square root of negative numbers. So, x values are restricted for f(x) = ✓x for real numbers and the domain is (0, infinity).
The complete question is attached.
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