To convert the fraction \( \frac{11}{5} \) to a decimal, we can follow the steps in your prompt.
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Understanding the problem: We need to express \( \frac{11}{5} \) in decimal form.
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Find how many tenths are there:
- We know that \( 5 \) ones is equivalent to \( 50 \) tenths. Therefore, let's consider \( \frac{11}{5} \) in terms of tenths.
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Divide tenths by 11: \[ 50 \text{ tenths} \div 11 \] Let's perform the long division:
- How many times does 11 fit into 50?
- \( 11 \times 4 = 44 \)
- \( 11 \times 5 = 55 \) (too much)
- So \( 11 \) fits into \( 50 \) a total of \( 4 \) times.
- How many times does 11 fit into 50?
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Multiply and subtract:
- Now, \( 11 \times 4 = 44 \)
- Subtract: \[ 50 - 44 = 6 \] So, after dividing, we have \( 4 \) tenths with \( 6 \) tenths remaining.
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Bringing down the next digit: Since we are looking for a decimal, we can continue.
- Take the remainder \( 6 \) (as \( 6.0 \)), and consider it as \( 60 \) tenths (adding a zero to continue the division).
- \( 60 \div 11 \):
- Fits \( 5 \) times, since \( 11 \times 5 = 55 \).
- Subtract: \[ 60 - 55 = 5 \]
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Continue this process:
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Bring down another \( 0 \) making it \( 50 \) again.
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From here, we see a pattern emerging:
- \( 50 \div 11 = 4 \) with a remainder of \( 6 \).
- This repeats continuously, giving you \( 0.4 \) and then another \( 5 \), back to \( 50 \).
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Putting this all together, we get: \[ \frac{11}{5} = 2.2 \]
Thus, the final answer is: \[ \frac{11}{5} = 2.2 \]
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