On dividing 0.86 by 16.564, the actual answer is 0.0519198. The correctly reported answer will be

Options

A. `0.05`
B. `0.051`
C. `0.0519`
D. `0.05191`

Answer

To solve the problem of dividing 0.86 by 16.564 and determining the correctly reported answer based on significant figures, we can follow these steps:

### Step 1: Perform the Division
Calculate the division of 0.86 by 16.564.

\[ \text{Result} = \frac{0.86}{16.564} = 0.0519198 \]

### Step 2: Identify Significant Figures
Next, we need to identify the number of significant figures in the original numbers (0.86 and 16.564).

- **0.86** has **2 significant figures** (the digits 8 and 6).
- **16.564** has **5 significant figures** (the digits 1, 6, 5, 6, and 4).

### Step 3: Determine the Limiting Significant Figures
When performing calculations, the result should be reported with the same number of significant figures as the measurement with the least number of significant figures. In this case, 0.86 has the least number of significant figures (2).

### Step 4: Round the Result
Now, we need to round the result (0.0519198) to 2 significant figures.

- The first two significant figures in 0.0519198 are 5 and 1.
- The third digit (9) is greater than 5, which means we round up the second significant figure.

Thus, rounding 0.0519198 to 2 significant figures gives us:

\[ 0.0519 \]

### Step 5: Report the Final Answer
Since we need to report the answer with 2 significant figures, we can express it as:

\[ \text{Correctly reported answer} = 0.051 \]

### Final Answer
The correctly reported answer will be **0.051**.

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