To convert \( 5 \frac{3}{16} \) to a decimal using long division, we can first convert the mixed number into an improper fraction.
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Convert \( 5 \) into a fraction: \( 5 = \frac{5 \times 16}{16} = \frac{80}{16} \)
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Add \( \frac{3}{16} \) to \( \frac{80}{16} \):
\( 5 \frac{3}{16} = \frac{80}{16} + \frac{3}{16} = \frac{83}{16} \)
Now we will perform long division to convert \( \frac{83}{16} \) into a decimal.
- Divide \( 83 \) by \( 16 \):
- \( 16 \) goes into \( 83 \) \( 5 \) times (since \( 16 \times 5 = 80 \)).
- Subtract \( 80 \) from \( 83 \), which leaves a remainder of \( 3 \).
Now, we bring down a \( 0 \) to continue the division:
- This makes it \( 30 \).
- \( 16 \) goes into \( 30 \) \( 1 \) time (since \( 16 \times 1 = 16 \)).
- Subtract \( 16 \) from \( 30 \), which leaves a remainder of \( 14 \).
Bring down another \( 0 \) to make \( 140 \):
- \( 16 \) goes into \( 140 \) \( 8 \) times (since \( 16 \times 8 = 128 \)).
- Subtract \( 128 \) from \( 140 \), which leaves a remainder of \( 12 \).
Bring down another \( 0 \):
- \( 16 \) goes into \( 120 \) \( 7 \) times (since \( 16 \times 7 = 112 \)).
- Subtract \( 112 \) from \( 120 \), which leaves a remainder of \( 8 \).
Bring down another \( 0 \):
- \( 16 \) goes into \( 80 \) \( 5 \) times (since \( 16 \times 5 = 80 \)).
- Subtract \( 80 \) from \( 80 \), which leaves a remainder of \( 0 \).
Putting it all together, \( 83 ÷ 16 = 5.1875 \).
Thus, \( 5 \frac{3}{16} \) as a decimal is:
5.1875