Solve:
`1.0971 div 0.069`

Answer

To solve the problem \( 1.0971 \div 0.069 \), we can follow these steps:

### Step 1: Remove the Decimals
To simplify the division, we can eliminate the decimal points. We do this by multiplying both the numerator and the denominator by 1000 (since 0.069 has 3 decimal places).

\[ 1.0971 \div 0.069 = \frac{1.0971 \times 1000}{0.069 \times 1000} = \frac{1097.1}{69} \]

### Step 2: Set Up the Long Division
Now, we will perform long division of 1097.1 by 69. We can ignore the decimal for now and consider 10971 (by treating it as 10971 instead of 1097.1).

### Step 3: Divide the First Part
Start with the first part of the number. How many times does 69 go into 109?

69 goes into 109 **1 time** (since \( 69 \times 1 = 69 \)).

Subtract \( 69 \) from \( 109 \):
\[ 109 - 69 = 40 \]

### Step 4: Bring Down the Next Digit
Now, bring down the next digit (which is 7) to make it 407.

### Step 5: Divide Again
Now, how many times does 69 go into 407?

69 goes into 407 **5 times** (since \( 69 \times 5 = 345 \)).

Subtract \( 345 \) from \( 407 \):
\[ 407 - 345 = 62 \]

### Step 6: Bring Down the Next Digit
Now, bring down the next digit (which is 1) to make it 621.

### Step 7: Divide Again
Now, how many times does 69 go into 621?

69 goes into 621 **9 times** (since \( 69 \times 9 = 621 \)).

Subtract \( 621 \) from \( 621 \):
\[ 621 - 621 = 0 \]

### Step 8: Combine the Results
So far, we have:
- 1 (from the first division)
- 5 (from the second division)
- 9 (from the third division)

This gives us \( 159 \).

### Step 9: Adjust for the Decimal
Now we need to adjust for the decimal places. We originally had 4 decimal places in 1.0971 and 3 decimal places in 0.069.

Thus, we have \( 4 - 3 = 1 \) decimal place to account for in our answer.

So, we place the decimal point:
\[ 159 \rightarrow 15.9 \]

### Final Answer
The final answer is:
\[ \boxed{15.9} \]

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