Let's go through each number one by one and determine the number of significant figures:

1. 0.004073

• The leading zeros are not significant. The significant figures are the non-zero digits and any zeros between them or following them in a decimal context.
• Significant digits: 4, 0, 7, 3
• Number of significant figures = 4

2. 670000

• There is no decimal point shown, so the trailing zeros are not considered significant in this case.
• Significant digits: 6, 7
• Number of significant figures = 2

3. 3.50 x 10²

• This is in scientific notation, and any digits written explicitly before the exponent are significant.
• Significant digits: 3, 5, 0
• Number of significant figures = 3

4. 12.0 x 10³

• Similarly, in scientific notation, the digits before the exponent are significant, including any trailing zeros after a decimal point.
• Significant digits: 1, 2, 0
• Number of significant figures = 3

5. 78042.00

• The trailing zeros after the decimal point are significant because they indicate precision.
• Significant digits: 7, 8, 0, 4, 2, 0, 0
• Number of significant figures = 7

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Would you like more explanation on how significant figures work in these cases? Or do you have any other questions?

Further questions:

1. What are the rules for determining significant figures in scientific notation?
2. How do trailing zeros in numbers without a decimal point affect the count of significant figures?
3. What is the significance of significant figures in scientific measurements?
4. How would the number of significant figures change if 670000 were written as 6.70000 × 10⁵?
5. How does the precision of a measurement relate to the number of significant figures?

Tip: When a number is written in scientific notation, all digits in the coefficient (the part before the × 10^n) are significant.