Question

Convert 0.5¯¯¯
0.
5
¯
to a fraction.(1 point)
The fraction equivalent of 0.5¯¯¯ is
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ℎ
𝑒

𝑓
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𝑡
𝑖
𝑜
𝑛

𝑒
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𝑖
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𝑜
𝑓

0.
5
¯

𝑖
Answer
less words and symbols
Answer
dumb tht down
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step by step
Answer
less steps
Answered by GPT-4o mini
To convert the repeating decimal \( 0.5\overline{5} \) (which is \( 0.5555\ldots \)) to a fraction, we can follow these steps:

1. Let \( x = 0.5\overline{5} \).
2. Multiply both sides of the equation by 10 to shift the decimal point:
\[
10x = 5.5555\ldots
\]
3. Now, subtract the original \( x \) from this new equation:
\[
10x - x = 5.5555\ldots - 0.5555\ldots
\]
\[
9x = 5
\]
4. Solve for \( x \):
\[
x = \frac{5}{9}
\]

Thus, the fraction equivalent of \( 0.5\overline{5} \) is \( \frac{5}{9} \).
Answered by GPT-4o mini
To convert \( 0.5\overline{5} \) to a fraction:

1. Let \( x = 0.5\overline{5} \).
2. Multiply by 10: \( 10x = 5.5555\ldots \).
3. Subtract: \( 10x - x = 5.5555\ldots - 0.5555\ldots \).
4. Result: \( 9x = 5 \).
5. Thus, \( x = \frac{5}{9} \).

The fraction is \( \frac{5}{9} \).
Answered by GPT-4o mini
To convert \( 0.5\overline{5} \) to a fraction:

1. Let \( x = 0.5\overline{5} \).
2. Move the decimal: \( 10x = 5.5555\ldots \).
3. Subtract: \( 10x - x = 5.5555\ldots - 0.5555\ldots \).
4. So, \( 9x = 5 \).
5. Divide: \( x = \frac{5}{9} \).

So, \( 0.5\overline{5} = \frac{5}{9} \).
Answered by GPT-4o mini
Sure! Here’s a step-by-step breakdown to convert \( 0.5\overline{5} \) to a fraction:

### Step 1: Define the Decimal
Let:
\[
x = 0.5\overline{5}
\]
This means \( x = 0.5555\ldots \)

### Step 2: Multiply by 10
Multiply both sides of the equation by 10 to move the decimal point:
\[
10x = 5.5555\ldots
\]

### Step 3: Write the Subtraction
Now, we have two equations:
1. \( x = 0.5555\ldots \)
2. \( 10x = 5.5555\ldots \)

Subtract the first equation from the second:
\[
10x - x = 5.5555\ldots - 0.5555\ldots
\]

### Step 4: Simplify the Left Side
On the left side, you simplify:
\[
9x = 5
\]

### Step 5: Solve for \( x \)
Now, divide both sides by 9:
\[
x = \frac{5}{9}
\]

### Conclusion
So, the fraction equivalent of \( 0.5\overline{5} \) is:
\[
\frac{5}{9}
\]
Answered by GPT-4o mini
Sure! Here’s a simplified version with fewer steps:

1. Let \( x = 0.5\overline{5} \).
2. Multiply by 10: \( 10x = 5.5555\ldots \).
3. Subtract the first equation from the second:
\[
10x - x = 5.5555\ldots - 0.5555\ldots \implies 9x = 5
\]
4. Divide by 9:
\[
x = \frac{5}{9}
\]

So, \( 0.5\overline{5} = \frac{5}{9} \).