Final answer:
After evaluating the given expression and considering the powers of 10, the sum of (2.92 × 10^6) and (4 × 10^{-2}) remains approximately 2.92 × 10^6 in standard form, as the second term is negligible in this context.
Step-by-step explanation:
To calculate the value of (2.92 × 106) + (4 × 10–2) and express it in standard form, we need to perform addition while taking into account the different exponents of 10.
Firstly, we write both numbers in scientific notation, if they are not already. This means we write them as a product of a number between 1 and 10, and a power of 10. The first number is already in scientific notation; the second one is also already in scientific notation.
Let's convert the second term to the power of 10 that matches the first term for easy addition:
- 4 × 10–2 = 0.04 = 0.04 × 106 / 108 = 4 × (100 × 106) / 108 = 4 × 106 / 108
Next, we perform the addition of the two terms:
- (2.92 × 106) + (4 × 10–2) = (2.92 × 106) + (4 × 106 / 108) = 2.92 + 0.00000004 = 2.92000004
Since the term 4 × 10–2 is so much smaller than 2.92 × 106, it has a negligible effect when added, and the summation in standard form is approximately equal to the first term.
Finally, the answer in scientific notation is 2.92000004 × 106. However, given the significant figures involved, we can round this to 2.92 × 106, which is the more accurate representation of the sum concerning the original number's precision.