Question

The numbers \(17.0145\) and \(21.0235\) were rounded to three figures after the decimal point. The resulting numbers, respectively, are

• A. \(17.015\) and \(21.024\)
• B. \(17.014\) and \(21.023\)
• C. \(17.015\) and \(21.023\)
• D. \(17.014\) and \(21.024\)

Hint:

Scientific Rounding Rule for a terminal 5: - \(\text{Even} + 5 \rightarrow \text{Stays Same}\) (e.g., \(45 \rightarrow 4\)) - \(\text{Odd} + 5 \rightarrow \text{Rounds Up}\) (e.g., \(35 \rightarrow 4\)) This protocol minimizes cumulative statistical skew in large experimental datasets.

Answer 1

The Correct Option is D

Step 1: State the rounding rule.
We round to three places after the decimal. When the digit just after the keep-position is exactly 5 with nothing meaningful after it, we use the round-to-even rule: keep the retained digit unchanged if it is even, and raise it by one if it is odd.
Step 2: Set up the first number 17.0145.
Keeping three decimals means keeping \(17.014\) and looking at the next digit, which is \(5\).
Step 3: Apply the rule to 17.0145.
The retained digit is \(4\), which is even, so it stays the same. The result is \(17.014\).
Step 4: Set up the second number 21.0235.
Keeping three decimals means keeping \(21.023\) and looking at the next digit, which is \(5\).
Step 5: Apply the rule to 21.0235.
The retained digit is \(3\), which is odd, so it goes up by one to \(4\). The result is \(21.024\).
Step 6: Combine the answers.
The rounded numbers are \(17.014\) and \(21.024\), which is option 4.
\[ \boxed{17.014 \text{ and } 21.024} \]