Solve:
`6.206 div 10.7`

Answer

To solve the problem \(6.206 \div 10.7\), we will follow these steps:

### Step 1: Eliminate the Decimal Points
To make the division easier, we will eliminate the decimal points by multiplying both the dividend (6.206) and the divisor (10.7) by the same power of 10. Since 10.7 has one decimal place, we will multiply both by 10.

\[ 6.206 \times 10 = 62.06 \]
\[ 10.7 \times 10 = 107 \]

Now, we rewrite the division as:
\[ 62.06 \div 107 \]

### Step 2: Set Up the Long Division
We will set up the long division with 107 outside the division bracket and 62.06 inside.

### Step 3: Determine How Many Times 107 Fits into 620
Since 107 does not fit into 62, we consider how many times it fits into 620.

1. **Finding the multiples of 107:**
- \(107 \times 1 = 107\)
- \(107 \times 2 = 214\)
- \(107 \times 3 = 321\)
- \(107 \times 4 = 428\)
- \(107 \times 5 = 535\)
- \(107 \times 6 = 642\) (too high)

The largest multiple of 107 that fits into 620 is \(107 \times 5 = 535\).

### Step 4: Perform the Subtraction
Now we subtract 535 from 620:
\[ 620 - 535 = 85 \]

### Step 5: Bring Down the Next Digit
Next, we bring down the next digit from 62.06, which is 6, making it 856.

### Step 6: Determine How Many Times 107 Fits into 856
Now we need to see how many times 107 fits into 856.

1. **Finding the multiples of 107:**
- \(107 \times 8 = 856\)

So, 107 fits into 856 exactly 8 times.

### Step 7: Perform the Subtraction Again
Now we subtract 856 from 856:
\[ 856 - 856 = 0 \]

### Step 8: Write the Final Answer
Now we can write the result of the division. Since we placed a decimal point after the 0 (from the first part of the division), the final answer is:
\[ 0.58 \]

Thus, the solution to \(6.206 \div 10.7\) is:
\[ \boxed{0.58} \]

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