To convert \( 5 \frac{3}{16} \) to a decimal using long division, we will first convert the mixed number to an improper fraction and then divide:
-
Convert \( 5 \frac{3}{16} \) to an improper fraction:
\[ 5 \frac{3}{16} = \frac{5 \times 16 + 3}{16} = \frac{80 + 3}{16} = \frac{83}{16} \]
-
Now, perform the division \( 83 \div 16 \):
- How many times does 16 go into 83?
- \( 16 \times 5 = 80 \), so it goes 5 times.
- Calculate the remainder: \[ 83 - 80 = 3 \]
- So, \( 83 \div 16 = 5 \) with a remainder of 3.
- How many times does 16 go into 83?
-
Now we need to convert the remainder into a decimal:
- Take the remainder (3), and append a decimal point, making it \( 3.0 \).
- We can rewrite \( 3.0 \div 16 \) and divide:
- \( 16 \) goes into \( 30 \): It goes \( 1 \) time (because \( 16 \times 1 = 16 \)).
- The remainder is \( 30 - 16 = 14 \).
- Now take down another \( 0 \), making it \( 140 \).
- \( 16 \) goes into \( 140 \) \( 8 \) times (because \( 16 \times 8 = 128 \)).
- The remainder is \( 140 - 128 = 12 \).
- Take down another \( 0 \), making it \( 120 \).
- \( 16 \) goes into \( 120 \) \( 7 \) times (because \( 16 \times 7 = 112 \)).
- The remainder is \( 120 - 112 = 8 \).
- Take down another \( 0 \), making it \( 80 \).
- \( 16 \) goes into \( 80 \) \( 5 \) times (because \( 16 \times 5 = 80 \)).
- The remainder is \( 80 - 80 = 0 \).
Thus, when we combine the results, we have:
\[ 83 \div 16 = 5.1875 \]
The complete decimal representation of \( 5 \frac{3}{16} \) is \( 5.1875 \).
Therefore, the correct answer is:
5.1875