The sum of the numbers 436.32, 227.2 and 0.301 in appropriate significant figures is

The correct option is 664.

To understand why this is the correct answer, we can break down the process of addition and the application of significant figure rules step-by-step.

Step 1: Perform the basic addition
First, we find the arithmetic sum of the three given numbers:

$436.32+227.2+0.301=663.821$

Step 2: Determine the number of significant figures
Next, we count the significant figures in each of the given numbers:
1. 436.32 contains 5 significant figures.
2. 227.2 contains 4 significant figures.
3. 0.301 contains 3 significant figures (the leading zero before the decimal point is not significant).

Step 3: Apply the rounding rule
Under the rule for operations where the total precision is governed by the least precise number, we round the final sum to the same number of significant figures as the number with the fewest significant figures.
Here, 0.301 has the fewest significant figures (3). Therefore, we round our total sum of 663.821 to 3 significant figures.

Rounding 663.821 to 3 significant figures:
The third significant figure is 3 (in the units place), and the digit following it is 8. Since 8 is greater than or equal to 5, we round up the 3 to 4.

$663.821\to 664$

This gives us the final result of 664.