In chemistry, understanding significant figures is crucial for accurate calculations, especially when performing multiplication and division. The key principle to remember is that the final answer should reflect the least number of significant figures from the values used in the calculation.
For example, consider the multiplication of three values: 3.16, 0.003027, and \(5.7 \times 10^{-3}\). To determine the number of significant figures in each value, we start counting from the first non-zero digit:
- For 3.16, the first non-zero digit is 3, and counting from there gives us 3 significant figures.
- For 0.003027, the first non-zero digit is 3, leading to 4 significant figures.
- For \(5.7 \times 10^{-3}\), we focus on the coefficient 5.7, which has 2 significant figures.
Now, we identify the least number of significant figures among these values, which is 2. Therefore, our final answer must also contain 2 significant figures.
After performing the multiplication, we initially obtain \(5.4522324 \times 10^{-5}\). To express this with 2 significant figures, we look at the first two digits, 5 and 4. The next digit is 5, which prompts us to round up the 4 to 5. Thus, the final answer is \(5.5 \times 10^{-5}\), ensuring it adheres to the significant figures rule based on the original values.
Having covered multiplication and division, it is essential to explore how significant figures apply to addition and subtraction in subsequent calculations.