To convert the mixed number \( 5 \frac{3}{16} \) to a decimal using long division, follow these steps:
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Convert the mixed number to an improper fraction: To do this, multiply the whole number by the denominator and add the numerator. \[ 5 \frac{3}{16} = \frac{(5 \times 16) + 3}{16} = \frac{80 + 3}{16} = \frac{83}{16} \]
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Perform long division to convert \( \frac{83}{16} \) to a decimal: Divide 83 by 16.
- 16 goes into 83 a total of 5 times (since \( 16 \times 5 = 80 \)).
- Subtract 80 from 83 which leaves you with a remainder of 3. \[ 83 - 80 = 3 \]
Now bring down a zero to continue the division.
- Now you're dividing 30 by 16.
- 16 goes into 30 once (since \( 16 \times 1 = 16 \)).
- Subtract 16 from 30 which leaves you with a remainder of 14. \[ 30 - 16 = 14 \]
Bring down another zero to get 140.
- 16 goes into 140 eight times (since \( 16 \times 8 = 128 \)).
- Subtract 128 from 140 which leaves you with a remainder of 12. \[ 140 - 128 = 12 \]
Bring down another zero to get 120.
- 16 goes into 120 seven times (since \( 16 \times 7 = 112 \)).
- Subtract 112 from 120 which leaves you with a remainder of 8. \[ 120 - 112 = 8 \]
Bring down another zero to get 80.
- 16 goes into 80 five times (since \( 16 \times 5 = 80 \)).
- Subtract 80 from 80 which leaves you with a remainder of 0. \[ 80 - 80 = 0 \]
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Combine the results: From the division, we have:
- \( 5 \) (the integer part),
- \( 1 \) (from the first decimal place),
- \( 8 \) (from the second decimal place),
- \( 7 \) (from the third decimal place),
- \( 5 \) (from the fourth decimal place).
Thus, \( 5 \frac{3}{16} = 5.1875 \).
So the answer is \( \boxed{5.1875} \).
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