Evaluate:
`478.4 div 416`

Answer

To evaluate \( 478.4 \div 416 \), we can follow these steps:

### Step 1: Convert the division into a fraction
We can express the division as a fraction:
\[ \frac{478.4}{416} \]

### Step 2: Eliminate the decimal
To eliminate the decimal in the numerator, we can multiply both the numerator and the denominator by 10:
\[ \frac{478.4 \times 10}{416 \times 10} = \frac{4784}{4160} \]

### Step 3: Perform the division
Now we need to divide \( 4784 \) by \( 4160 \).

1. Since \( 4784 \) is slightly larger than \( 4160 \), we can start by dividing:
\[ 4784 \div 4160 = 1 \]
- Multiply \( 1 \) by \( 4160 \):
\[ 1 \times 4160 = 4160 \]
- Subtract to find the remainder:
\[ 4784 - 4160 = 624 \]

### Step 4: Add decimal point and zero
Since the remainder \( 624 \) is less than \( 4160 \), we add a decimal point and a zero to the remainder:
\[ 6240 \]

### Step 5: Divide again
Now we divide \( 6240 \) by \( 4160 \):
1. Since \( 6240 \) is still less than \( 8320 \) (which is \( 4160 \times 2 \)), we multiply by \( 1 \):
\[ 1 \times 4160 = 4160 \]
- Subtract to find the new remainder:
\[ 6240 - 4160 = 2080 \]

### Step 6: Add another zero
Again, since \( 2080 \) is less than \( 4160 \), we add another zero:
\[ 20800 \]

### Step 7: Divide again
Now we divide \( 20800 \) by \( 4160 \):
1. We can see that \( 4160 \times 5 = 20800 \):
\[ 5 \times 4160 = 20800 \]
- Subtract to find the remainder:
\[ 20800 - 20800 = 0 \]

### Final Answer
Since there is no remainder left, we can conclude:
\[ 478.4 \div 416 = 1.15 \]