To determine the number of significant figures in the expression [tex]\((3.50 + 450) \times 10^5\)[/tex], we need to follow these steps:
1. Identify significant figures in the numbers:
- [tex]\(3.50\)[/tex] has 3 significant figures. The digits 3 and 5 are significant, and the trailing zero after the decimal point is also significant.
- [tex]\(450\)[/tex] has 3 significant figures. The digits 4 and 5 are significant, and the trailing zero is considered significant in this context.
2. Add the numbers while considering significant figures:
- When adding [tex]\(3.50\)[/tex] and [tex]\(450\)[/tex], we should consider the discrepancy in their decimal places. However, in terms of significant figures, we focus on the least precise number.
- The result of [tex]\(3.50 + 450\)[/tex] would be [tex]\(453.50\)[/tex], but for significant figures, we consider\ the significant figure rule of the least precise measurement, [tex]\(450\)[/tex], with 3 significant figures. Therefore, the sum [tex]\(453.50\)[/tex] should be rounded to three significant figures, resulting in [tex]\(454\)[/tex].
3. Apply the scientific notation and multiplication:
- Multiplying [tex]\(454\)[/tex] by [tex]\(10^5\)[/tex] does not change the number of significant figures because [tex]\(10^5\)[/tex] is an exact number (a power of ten).
- Therefore, [tex]\(454 \times 10^5 = 4.54 \times 10^7\)[/tex].
4. Conclusion about significant figures:
- The result [tex]\(4.54 \times 10^7\)[/tex] retains the number of significant figures from [tex]\(454\)[/tex] which is 3 significant figures.
Thus, the number of significant figures in the expression [tex]\((3.50 + 450) \times 10^5\)[/tex] is:
[tex]\[
\boxed{3}
\][/tex]
