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

The correct option is 664.

To find the sum of the given numbers in appropriate significant figures, we follow these steps:

Step 1: Perform the basic addition
First, we find the direct sum of the three numerical values:\mathrm{}

436.32+227.2+0.301=663.821

Step 2: Determine the significant figures of each term
Next, we count the number of significant figures in each of the given values:
- 436.32 has 5 significant figures.
- 227.2 has 4 significant figures.
- 0.301 has 3 significant figures (the leading zero is not significant).

Step 3: Apply the rule for significant figures
The final result must be rounded to the same number of significant figures as the value with the least number of significant figures in the calculation.
Here, the least number of significant figures is 3 (from the number 0.301).

Step 4: Round off the final sum
We round the arithmetic sum, 663.821, to 3 significant figures:
- The first three significant digits are 6, 6, and 3.
- The next digit is 8, which is greater than 5, so we round up the preceding digit (3) by 1.
Rounding up gives us 664.