Sure, let's solve the given expression [tex]\( 25.5 \cdot 10.09 \)[/tex] while applying the rules of significant figures.
1. Identify the Significant Figures:
- For [tex]\( 25.5 \)[/tex]: It has 3 significant figures (2, 5, and 5).
- For [tex]\( 10.09 \)[/tex]: It has 4 significant figures (1, 0, 0, and 9).
2. Perform the Multiplication:
- Calculate [tex]\( 25.5 \times 10.09 \)[/tex].
- The result of this multiplication is [tex]\( 257.295 \)[/tex].
3. Determine the Appropriate Significant Figures for the Result:
- According to the rules of significant figures in multiplication, the result should be rounded to the same number of significant figures as the factor with the least number of significant figures.
- Here, [tex]\( 25.5 \)[/tex] has the least number of significant figures, which is 3.
4. Round the Result to 3 Significant Figures:
- To round [tex]\( 257.295 \)[/tex] to 3 significant figures, you look at the first three digits (2, 5, and 7) and consider the next digit (2) to decide whether to round up or down.
- Since the next digit (2) is less than 5, you round down, so [tex]\( 257.295 \)[/tex] remains [tex]\( 257.295 \)[/tex].
Thus, the final answer, rounded to 3 significant figures, remains [tex]\( 257.295 \)[/tex].
