To convert \( \frac{2}{9} \) to a decimal using long division, we can follow these steps:
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Set up the long division of 2 by 9. Since 2 is less than 9, we start by adding a decimal point and zeros (making it 2.000...).
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Divide 2.0 by 9. Since 9 can’t go into 2, we look at 20 (after putting a decimal point):
- 9 goes into 20 two times (because \( 9 \times 2 = 18 \)).
- Write 2 above the line.
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Subtract 18 from 20: \[ 20 - 18 = 2 \]
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Bring down the next 0 (to make it 20 again):
- Again, 9 goes into 20 two times (another \( 9 \times 2 = 18 \)).
- Write another 2 above the line.
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Subtract 18 from 20 again: \[ 20 - 18 = 2 \]
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This process will repeat indefinitely, yielding the digits 222..., which goes on forever.
Thus, \( \frac{2}{9} = 0.222...\)
To simplify \( 0.222...\) to one decimal place, we round it. Since the second decimal place (2) is less than 5, we round down.
Therefore, the value of \( \frac{2}{9} \) rounded to one decimal place is: \[ \boxed{0.2} \]
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