Express the result of the following calculation to the appropriate number of significant figures 3.24x0.08666/5.006

The correct option/answer is "0.561".

To determine the result of the calculation to the appropriate number of significant figures, we follow the rules for multiplication and division. Let's break down the process step-by-step:

Step 1: Identify the number of significant figures in each given value
Recall the rules for counting significant figures:
• Non-zero digits are always significant.
• Leading zeros (zeros before any non-zero digits) are not significant.
• Embedded zeros (zeros between non-zero digits) are significant.
• Trailing zeros in a number containing a decimal point are significant.

Let's apply these rules to each term in the calculation:
• 3.24: All three digits are non-zero, so it has 3 significant figures.
• 0.08666: The zeros at the beginning are leading zeros and are not significant. The digits 8, 6, 6, and 6 are significant. Thus, it has 4 significant figures.
• 5.006: The zeros are between non-zero digits (5 and 6), so they are significant. Thus, it has 4 significant figures.

Step 2: Determine the rule for multiplication and division
When multiplying and/or dividing numbers, the final result must be rounded to the same number of significant figures as the measurement with the least number of significant figures.
Comparing the count of significant figures from Step 1:
• 3.24 (3 significant figures)
• 0.08666 (4 significant figures)
• 5.006 (4 significant figures)
The term with the fewest significant figures is 3.24, which has 3 significant figures. Therefore, our final answer must be rounded to 3 significant figures.

Step 3: Perform the calculation
First, we carry out the calculation using the full precision of the numbers:

$$\frac{3.24\times 0.08666}{5.006}=\frac{0.2807784}{5.006}\approx \mathrm{0.5608837...}$$

Step 4: Round the result to 3 significant figures
We examine the raw result, 0.5608837...:
• The first three significant figures are 5, 6, and 0 (the leading zero is not significant).
• The digit immediately following our third significant figure (0) is 8.
• Since 8 is equal to or greater than 5, we round the preceding digit (0) up to 1.

Rounding 0.5608837... to three significant figures gives 0.561.