Question

After rounding \(1.245\) and \(1.235\) to three significant figures, we will have their answers respectively as

• A. \(1.24,\;1.23\)
• B. \(1.23,\;1.23\)
• C. \(1.23,\;1.24\)
• D. \(1.24,\;1.24\)

Hint:

When the digit to be dropped is exactly \(5\):
If the preceding digit is \textbf{even}, it is left unchanged.
If the preceding digit is \textbf{odd}, it is increased by 1. This rule is known as \textbf{rounding to even}.

Answer 1

The Correct Option is D

Step 1: Rounding \(1.245\) to three significant figures. The first three significant digits are \(1.24\). The next digit is \(5\). Using the round-to-even rule, since the last retained digit \(4\) is even, it remains unchanged. \[ 1.245 \approx 1.24 \]
Step 2: Rounding \(1.235\) to three significant figures. The first three significant digits are \(1.23\). The next digit is \(5\). The last retained digit \(3\) is odd, so it is increased by 1. \[ 1.235 \approx 1.24 \]
Step 3: Therefore, the rounded values are: \[ 1.245 \rightarrow 1.24,\qquad 1.235 \rightarrow 1.24 \]