To convert \( \frac{6}{32} \) to a decimal using long division, follow these steps:
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Set up the long division: You will divide 6 by 32. Since 6 is less than 32, you need to add a decimal point and a zero. This means you consider 6.0 (or 60).
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Divide: Determine how many times 32 goes into 60.
- 32 goes into 60 once (1).
- Write 1 above the division bar.
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Multiply: Multiply 1 by 32, which gives 32.
- Write 32 below 60.
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Subtract: Subtract 32 from 60.
- \( 60 - 32 = 28 \)
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Bring down the next zero: Since there's still a decimal point needed, we bring down a 0 to make it 280.
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Repeat the division: Now, determine how many times 32 goes into 280.
- 32 goes into 280 eight times (8).
- Write 8 next to the 1 above the division bar.
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Multiply again: Multiply 8 by 32, which gives 256.
- Write 256 below 280.
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Subtract: Subtract 256 from 280.
- \( 280 - 256 = 24 \)
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Bring down another zero: Now bring down another zero, making it 240.
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Repeat the division: Determine how many times 32 goes into 240.
- 32 goes into 240 seven times (7).
- Write 7 next to the 18 above the division line.
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Multiply again: Multiply 7 by 32, which gives 224.
- Write 224 below 240.
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Subtract: Subtract 224 from 240.
- \( 240 - 224 = 16 \)
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Bring down the next zero: Bring down another zero to make it 160.
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Repeat the process: Determine how many times 32 goes into 160.
- 32 goes into 160 five times (5).
- Write 5 next to the previous digit above the division line.
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Multiply again: Multiply 5 by 32, which gives 160.
- Write 160 below 160.
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Subtract: Subtract 160 from 160.
- \( 160 - 160 = 0 \)
Now that the remainder is 0, we finish our long division.
Putting it all together, the result of \( \frac{6}{32} \) is \( 0.1875 \).
Thus, \( \frac{6}{32} = 0.1875 \).