Express 302.10495 correct to five significant figures

Analyze the question: We need to round 302.10495 to 5 significant figures.

Concept: Significant figures count from the first non-zero digit, and zeros between non-zero digits count too. To round, look at the digit right after the last digit you keep. If it is 5 or more, round up. If it is less than 5, leave the last kept digit unchanged.

Solution:

Digits of 302.10495, counted from the left:

1. 3
2. 0
3. 2
4. 1
5. 0
6. 4
7. 9
8. 5

The first 5 significant figures are 3, 0, 2, 1, 0, which gives 302.10.

The next digit (the 6th significant figure) is 4. Since 4 is less than 5, we do not round up. The 9 and 5 that follow do not matter. Rounding is decided only by the digit immediately after the cut-off. Rounding in steps (0.10495 → 0.1050 → 0.105) is a common mistake and gives a wrong result.

So 302.10495 ≈ 302.10 (5 s.f.)

Check the other options:

• B (302.11) is what you get by wrongly rounding in steps, or by treating it as 4 s.f.
• C (302.105) has 6 significant figures.
• D (302.1049) has 7 significant figures.

Only A has exactly 5 significant figures and is correctly rounded.

Tip: Never round in stages. Find the cut-off point, look only at the very next digit, and decide once. Also remember that the trailing zero in 302.10 must be kept, because it is a significant figure.