Taking into account the significant figures, what is the value of 9.99 m + 0.0099 m

The correct answer is 10.00 m.

To find the sum of the measurements while respecting the rules of significant figures, we follow a two-step process: performing the standard addition and then rounding the result according to the rules of significant figures for addition and subtraction.

Step 1: Perform the basic addition
First, we add the two numbers together as we normally would:

$9.99\text{m}+0.0099\text{m}=9.9999\text{m}$

Step 2: Apply the rule for addition and subtraction of significant figures
When adding or subtracting quantities, the final result must be rounded so that it has the same number of decimal places as the starting measurement with the fewest decimal places (the least precise measurement). Let us determine the number of decimal places for each value:
- 9.99 m has 2 decimal places.
- 0.0099 m has 4 decimal places.

Since the fewest decimal places among the two values is 2, the final sum must be rounded to exactly 2 decimal places (the hundredths place).

Step 3: Round the result to the correct number of decimal places
Rounding 9.9999 m to two decimal places:
- The digit in the second decimal place (hundredths) is 9.
- The digit immediately to its right (thousandths) is 9, which is greater than or equal to 5, meaning we round up.
- Rounding up 9.9999 m to the hundredths place yields:

$10.00\text{m}$

Thus, taking into account the significant figures, the correct value is 10.00 m.