approximate 0.0033780 to 3 significant figures

Analyze the question: We need to round 0.0033780 to 3 significant figures.

Concept: Significant figures start counting from the first non-zero digit. Leading zeros (the zeros before the first non-zero digit) are only placeholders and are not counted.

Solution:

1. Write the number: 0.0033780
2. Leading zeros: 0.00 are not significant.
3. The significant digits start at the first 3: 3, 3, 7, 8, 0
4. We need 3 significant figures: 3, 3, 7
5. Look at the next digit (the 4th significant figure), which is 8. Since 8 ≥ 5, we round the last kept digit up: 7 becomes 8.
6. So we get 3, 3, 8, which gives 0.00338

Check the options:

• A. 338 is the wrong magnitude (the value is far too large).
• B. 0.338 is also the wrong magnitude.
• C. 0.00338 is correct.
• D. 0.003 is only 1 significant figure.

Tip: For significant figures, always ignore the leading zeros, count from the first non-zero digit, then check the next digit to decide whether to round up (5 or more) or leave it unchanged (4 or less). Also make sure the decimal place is preserved so the size of the number stays the same.