What’s 0.45 recurring 5 as a fraction in its simplest form? a) 9/20 b) 4/9 c) 5/11 d) 1/2
The Correct Answer and Explanation is :
To convert (0.45\overline{5}) (0.455555…) into a fraction, follow these steps:
Step 1: Let (x = 0.45\overline{5})
Let (x) be equal to the repeating decimal:
[
x = 0.4555555\ldots
]
Step 2: Multiply by 10 to shift the decimal
Since the repeating part (5) starts after one digit, multiply both sides of the equation by 10:
[
10x = 4.555555\ldots
]
Now, subtract the original equation (Step 1) from this new equation:
[
10x – x = (4.555555\ldots) – (0.455555\ldots)
]
This simplifies to:
[
9x = 4.1
]
Step 3: Solve for (x)
Now, express (4.1) as a fraction:
[
4.1 = \frac{41}{10}
]
So the equation becomes:
[
9x = \frac{41}{10}
]
Now solve for (x) by dividing both sides by 9:
[
x = \frac{41}{10 \times 9} = \frac{41}{90}
]
Step 4: Simplify the fraction
The fraction (\frac{41}{90}) is already in its simplest form because 41 is a prime number and does not share any common factors with 90.
Thus, the fraction form of (0.45\overline{5}) is:
[
\boxed{\frac{41}{90}}
]
Step 5: Verify the answer choices
None of the given options (a) 9/20, (b) 4/9, (c) 5/11, or (d) 1/2 matches the correct answer (\frac{41}{90}), so none of the choices are correct.