To convert the mixed number \(2 \frac{7}{16}\) to a decimal using long division, we can follow these steps:
-
Convert the mixed number to an improper fraction: \[ 2 \frac{7}{16} = \frac{2 \times 16 + 7}{16} = \frac{32 + 7}{16} = \frac{39}{16} \]
-
Set up the long division: We need to divide \(39\) by \(16\).
-
Perform the long division:
- Divide \(39\) by \(16\):
- \(16\) goes into \(39\) \(2\) times, because \(16 \times 2 = 32\).
- Subtract \(32\) from \(39\): \[ 39 - 32 = 7 \]
- Now, bring down a \(0\) (making it \(70\)):
- \(16\) goes into \(70\) \(4\) times, because \(16 \times 4 = 64\).
- Subtract \(64\) from \(70\): \[ 70 - 64 = 6 \]
- Bring down another \(0\) (turning it into \(60\)):
- \(16\) goes into \(60\) \(3\) times, because \(16 \times 3 = 48\).
- Subtract \(48\) from \(60\): \[ 60 - 48 = 12 \]
- Bring down another \(0\) (making it \(120\)):
- \(16\) goes into \(120\) \(7\) times, because \(16 \times 7 = 112\).
- Subtract \(112\) from \(120\): \[ 120 - 112 = 8 \]
- Bring down another \(0\) (making it \(80\)):
- \(16\) goes into \(80\) \(5\) times, because \(16 \times 5 = 80\).
- Subtract \(80\) from \(80\): \[ 80 - 80 = 0 \]
- Divide \(39\) by \(16\):
-
Combine the results:
- The quotient from the division is \(2.4375\), so: \[ 2 \frac{7}{16} = 2.4375 \]
Thus, the decimal representation of \(2 \frac{7}{16}\) is \( \boxed{2.4375} \).
1 answer