Express 0.0000407, correct to 2 significant figures

Analyze the question: We need to round 0.0000407 to 2 significant figures.

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

Solution:

1. Write the number: 0.0000407
2. Identify the first non-zero digit: 4. This is the 1st significant figure.
3. The next digit is 0, which is the 2nd significant figure (a zero between non-zero digits or after the first significant digit counts).
4. The next digit is 7, which is the 3rd significant figure. This is the digit we use to decide the rounding.

So, to 2 significant figures we keep "4" and "0", giving 0.000040. Since the next digit is 7 (5 or more), we round the last kept digit up: 0 becomes 1.

0.0000407 → 0.000041

Check: 0.000041 = 4.1 × 10⁻⁵, which has 2 significant figures (4 and 1). This matches the original number 4.07 × 10⁻⁵ rounded to 2 s.f.

Other options:

• A (0.0) has no significant figures.
• B (0.00004) has only 1 significant figure.
• D (0.0000407) has 3 significant figures.

Answer: C. 0.000041

Tip: Convert to standard form first: 4.07 × 10⁻⁵. Then rounding is easy, as you only deal with 4.07 → 4.1, and you avoid miscounting zeros.