Use long division to convert 3 and 4/5 to a decimal

Answer 1

To convert the mixed number \( 3 \frac{4}{5} \) to a decimal using long division, we can follow these steps:

1. Convert the mixed number to an improper fraction: \[ 3 \frac{4}{5} = \frac{(3 \times 5) + 4}{5} = \frac{15 + 4}{5} = \frac{19}{5} \]

2. Divide the numerator by the denominator using long division: We need to divide \( 19 \) by \( 5 \).

   • Step 1: How many times does \( 5 \) fit into \( 19 \)? It fits \( 3 \) times because \( 5 \times 3 = 15 \).
   • Step 2: Subtract \( 15 \) from \( 19 \): \[ 19 - 15 = 4 \]
   • Step 3: Since there is a remainder, we can add a decimal point and a zero, making it \( 40 \).
   • Step 4: Divide \( 40 \) by \( 5 \). \( 5 \) goes into \( 40 \) exactly \( 8 \) times because \( 5 \times 8 = 40 \).
   • Step 5: Subtract \( 40 \) from \( 40 \): \[ 40 - 40 = 0 \]

Since there is no remainder, the division process stops here.

3. Combine the results: The result of the long division gives us: \[ 19 \div 5 = 3.8 \] Therefore, the decimal representation of \( 3 \frac{4}{5} \) is \( 3.8 \).

So, \( 3 \frac{4}{5} = 3.8 \).