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

Concept: When rounding numbers to a specified number of decimal places, standard scientific rounding rules (often called the round-to-nearest-even rule or bankers' rounding) apply to eliminate rounding bias when the digit to be dropped is exactly 5.

Rules for rounding when the trailing digit is exactly 5:

• Identify the last digit to be retained (the target place).

• Look at the digit immediately following it. If that next digit is exactly \(5\) (with no non-zero digits following it): itemize

• If the digit to be retained is

even, leave it unchanged.

• If the digit to be retained is

odd, increase it by \(1\) to make it even.
itemize

Step 1: Rounding the value \(17.0145\)
We want to round to three figures after the decimal point.

• The third digit after the decimal point is

\(4\).

• The digit immediately following it is

\(5\).

• We examine the value of our target third decimal digit: \(4\) is an

even number.

• Applying the rule for an even preceding digit, we leave it unchanged.

• Result: \(17.014\)

Step 2: Rounding the value \(21.0235\)
We want to round to three figures after the decimal point.

• The third digit after the decimal point is

\(3\).

• The digit immediately following it is

\(5\).

• We examine the value of our target third decimal digit: \(3\) is an

odd number.

• Applying the rule for an odd preceding digit, we increase it by 1 to make it even (\(3 + 1 = 4\)).

• Result: \(21.024\)
Combining our calculations, the rounded values are \(17.014\) and \(21.024\).