Question

The result of \(3.456+2.1\) with correct significant figures is:

• A. \(5.556\)
• B. \(5.56\)
• C. \(5.5\)
• D. \(5.6\)

Hint:

For addition and subtraction, round the final answer according to the least number of decimal places, not the least number of significant figures.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Significant figures represent the digits in a number that contribute to its measurement precision.
When performing mathematical operations, the precision of the result cannot be greater than the precision of the least precise measurement used.
For addition and subtraction, the rule is that the result must have the same number of decimal places as the measurement with the fewest decimal places.
Step 2: Detailed Explanation:
1. Examine the measurements provided:
- \( 3.456 \) has 3 decimal places.
- \( 2.1 \) has 1 decimal place.
2. Identify the limiting precision:
The number \( 2.1 \) is the least precise because it only provides information up to the tenths place.
Therefore, the final result must be rounded to one decimal place.
3. Perform the arithmetic operation:
\[ 3.456 + 2.1 = 5.556 \]
4. Apply the rounding rule:
We need to round 5.556 to the tenths place.
The digit in the tenths place is 5.
The digit following it (in the hundredths place) is 5.
Following the standard scientific rounding rule: if the digit following the rounding digit is 5 or greater, round up.
Since the next digit is 5 (and is followed by another non-zero digit 6), we increase the tenths place by 1.
Result \(\approx 5.6\).
Step 3: Final Answer:
The result with correct significant figures is 5.6.
This corresponds to Option (D).