To convert the mixed number \( 3 \frac{3}{8} \) to a decimal using long division, follow these steps:
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Convert the mixed number to an improper fraction. \( 3 \frac{3}{8} \) can be converted as follows: \[ 3 \frac{3}{8} = \frac{3 \times 8 + 3}{8} = \frac{24 + 3}{8} = \frac{27}{8} \]
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Perform long division of 27 by 8.
- Divide 27 by 8.
- 8 goes into 27 three times (since \( 8 \times 3 = 24 \)).
- Write 3 above the division line.
- Subtract \( 24 \) from \( 27 \), which gives you \( 3 \).
So far we have: \[ 3 \quad \text{(whole number part)} \]
Now we have a remainder of 3. To continue, we can add a decimal point and a zero (considering it as 30):
- Bring down a zero (turning the 3 into 30).
- 8 goes into 30 three times (since \( 8 \times 3 = 24 \)).
- Write 3 in the tenths place after the decimal point.
- Subtract \( 24 \) from \( 30 \), giving you \( 6 \).
So, at this point we have: \[ 3.3 \]
Now, take the 6 and add another zero (making it 60):
- 8 goes into 60 seven times (since \( 8 \times 7 = 56 \)).
- Write 7 in the hundredths place after the decimal point.
- Subtract \( 56 \) from \( 60 \), yielding \( 4 \).
Now we have: \[ 3.37 \]
Next, bring down another zero (making it 40):
- 8 goes into 40 five times (since \( 8 \times 5 = 40 \)).
- Write 5 in the thousandths place after the decimal point.
- Subtract \( 40 \) from \( 40 \), yielding \( 0 \).
This gives us the final result: \[ 3.375 \]
Thus, the decimal representation of \( 3 \frac{3}{8} \) is \( 3.375 \).
The correct response is: 3.375
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