Express the product of 0.007 and 0.057 to two significant figures

Step 1: Analyze the question We need to multiply 0.007 by 0.057, then round the result to 2 significant figures.

Step 2: Multiply Ignore the decimal points first: 7 × 57 = 399.

Count the decimal places: 0.007 has 3 and 0.057 has 3, so the product has 6 decimal places.

0.007 × 0.057 = 0.000399

Step 3: Round to 2 significant figures Significant figures start counting from the first non-zero digit. In 0.000399, the first non-zero digit is 3.

• 1st sig. fig: 3
• 2nd sig. fig: 9
• Next digit: 9, which is 5 or more, so we round the 9 up.

Rounding 39 up gives 40, so the result is 0.00040, which is 4.0 × 10⁻⁴.

Step 4: Match to the options 0.00040 = 0.0004 (the trailing zero is the same value). This matches option A.

Option B (0.00039) is a common trap. It is the result of truncating instead of rounding, and it is not correct because the digit after the 9 is another 9, which forces the round-up.

Answer: A. 0.0004

Exam tip: For significant figures, find the first non-zero digit, count from there, and look at the very next digit to decide whether to round up. Leading zeros never count. Also, when rounding 39x up to 40, remember that the value 0.00040 equals 0.0004.