Result (exact and with significant numbers)
\[ 2.96 + 8.1 + 5.0214 = 16.0814. \] Using the significant numbers rule for addition (round to the least number of decimal places), the reported value is: \[ 16.0814 \approx 16.1. \]
Interpreting “sign numbers” as significant numbers
The phrase “sign numbers” is interpreted here as significant numbers (significant figures) used in measurement reporting. The given expression contains only positive signed values (all are added), so the arithmetic sign handling is straightforward; the key additional idea is correct rounding for significant figures in addition.
Step 1: Compute the sum carefully
Add the first two terms.
\[ 2.96 + 8.1 = 11.06. \]
Add the third term.
\[ 11.06 + 5.0214 = 16.0814. \]
Step 2: Link the result with significant numbers (addition rule)
For addition and subtraction, the significant-figures rule is based on decimal places (not total significant digits):
Decimal-place rule (addition/subtraction)
The final result must be rounded to the fewest decimal places among the numbers being added.
| Number | Decimal places | Reason it matters |
|---|---|---|
| \(2.96\) | 2 | Measured to the hundredths place. |
| \(8.1\) | 1 | Measured to the tenths place (least precise in decimals). |
| \(5.0214\) | 4 | Measured to the ten-thousandths place. |
Identify the limiting precision.
The least number of decimal places is 1 (from 8.1), so the final sum must be rounded to one decimal place.
Round the exact sum to one decimal place.
\[ 16.0814 \approx 16.1 \] because the hundredths digit is 8, which rounds the tenths digit up.
Visualization: addition on a number line (exact sum and rounded sum)
Number line: \(2.96 \rightarrow 11.06 \rightarrow 16.0814 \approx 16.1\)
Final statement
The exact arithmetic sum is 16.0814, and when reported using significant numbers for addition (least decimal places), the correct rounded result is 16.1.