To convert \( \frac{6}{32} \) to a decimal using long division, we can follow these steps:
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Set up the long division: Divide 6 by 32. Since 6 is less than 32, we will add a decimal point and additional zeros to 6 to continue the division.
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Start the division:
- 32 goes into 60 (the first digit after extending 6 with a decimal) one time. So, we write 1 above the division bar.
- Multiply 1 by 32, which gives us 32. Subtract this from 60, which leaves us with 28.
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Bring down the next 0 to make it 280:
- 32 goes into 280 eight times (because 32 × 8 = 256). Write 8 above the division bar.
- Subtract 256 from 280, which leaves us with 24.
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Bring down another 0 to make it 240:
- 32 goes into 240 seven times (because 32 × 7 = 224). Write 7 above the division bar.
- Subtract 224 from 240, which leaves us with 16.
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Bring down another 0 to make it 160:
- 32 goes into 160 five times (because 32 × 5 = 160). Write 5 above the division bar.
- Subtract 160 from 160, which leaves us with 0.
Putting it all together, we have:
\[ 6 \div 32 = 0.1875 \]
So the decimal value of \( \frac{6}{32} \) is 0.1875.
The correct response is: 0.1875