To add [tex]\((7.405 \times 10^4) + (5.15 \times 10^{-6})\)[/tex], we need to carefully manage both terms in their respective forms before summing them up. Here is a step-by-step approach to reach the solution:
1. Express both numbers in standard decimal form:
- The first number, [tex]\(7.405 \times 10^4\)[/tex], can be written as [tex]\(74050\)[/tex]. In decimal notation, [tex]\( 7.405 \times 10^4\)[/tex] means moving the decimal point 4 places to the right.
- The second number, [tex]\(5.15 \times 10^{-6}\)[/tex], can be written as [tex]\(0.00000515\)[/tex]. In decimal notation, [tex]\(5.15 \times 10^{-6}\)[/tex] means moving the decimal point 6 places to the left.
2. Add the numbers in their standard form:
- [tex]\(74050 + 0.00000515 = 74050.00000515\)[/tex].
3. Express the result back in scientific notation if needed:
- The sum [tex]\(74050.00000515\)[/tex] is very close to [tex]\(74050\)[/tex], as the added smaller term doesn't change the significant digits much.
- To convert [tex]\(74050.00000515\)[/tex] back to scientific notation: it can be written as [tex]\(7.405000000515 \times 10^4\)[/tex], but usually, we keep significant figures concise. In this case, we retain it simply as [tex]\(74050.00000515\)[/tex].
Therefore, the final result, expressed in standard form, is [tex]\(74050.00000515\)[/tex].
