Let's break down the mathematical problems in this image and solve them step by step.

First Expression:

$1.00 \times 10^{-8} + 9.75 \times 10^4$

It has already been calculated as: $10.75 \times 10^4$

Second Expression:

$\frac{9.75 \times 10^4 + 5.47 \times 10^5}{1.79 \times 10^4}$

Step 1: Add the terms in the numerator: $9.75 \times 10^4 + 5.47 \times 10^5$ Convert $9.75 \times 10^4$ to $0.975 \times 10^5$: $0.975 \times 10^5 + 5.47 \times 10^5 = 6.445 \times 10^5$

Step 2: Divide by $1.79 \times 10^4$: $\frac{6.445 \times 10^5}{1.79 \times 10^4}$ Simplify: $\frac{6.445}{1.79} \times 10^{5-4} = 3.6 \times 10^1 = 36$

Third Expression:

$\frac{6.90 \times 10^{-5}}{\left(1.00 \times 10^{-8}\right) \left(9.75 \times 10^4\right)}$

Step 1: Multiply the terms in the denominator: $\left(1.00 \times 10^{-8}\right) \left(9.75 \times 10^4\right) = 9.75 \times 10^{-4}$

Step 2: Divide: $\frac{6.90 \times 10^{-5}}{9.75 \times 10^{-4}} = \frac{6.90}{9.75} \times 10^{-5 - (-4)}$ $\frac{6.90}{9.75} \times 10^{-1} \approx 0.7077 \times 10^{-1} = 7.08 \times 10^{-2}$

Final Results:

1. $10.75 \times 10^4$
2. $36$
3. $7.08 \times 10^{-2}$

Would you like detailed steps for any part? 😊

Related Questions:

1. What are the rules for adding and subtracting numbers in scientific notation?
2. How do you convert between different powers of 10 in scientific notation?
3. What happens when dividing powers of 10? Can it be applied universally?
4. How can we simplify fractions involving scientific notation?
5. Why do we prefer scientific notation for very large or small numbers?

Tip:

Always align the powers of 10 when adding or subtracting in scientific notation for consistency!