Let's convert the numbers given in the image into scientific notation:

1. $780,000$
   In scientific notation:
   $7.8 \times 10^5$

2. $83,256$
   In scientific notation:
   $8.3256 \times 10^4$

3. $0.225$
   In scientific notation:
   $2.25 \times 10^{-1}$

4. $0.000000678$
   In scientific notation:
   $6.78 \times 10^{-7}$

5. $0.0042 \times 10^3$
   This is already partly in scientific notation, but the $0.0042$ can be expressed as $4.2 \times 10^{-3}$, so the final notation becomes:
   $4.2 \times 10^0$
   Which is simply $4.2$.

6. $491 \times 10^{-5}$
   The $491$ can be written as $4.91 \times 10^2$, so the final expression becomes:
   $4.91 \times 10^{-3}$

7. $67,200 \times 10^{-9}$
   The $67,200$ can be written as $6.72 \times 10^4$, so the final notation is:
   $6.72 \times 10^{-5}$

Would you like further clarification or details about any of these conversions?

Here are 5 related questions to deepen your understanding:

1. What is scientific notation and why is it useful in expressing large or small numbers?
2. How would you convert negative powers of 10 in scientific notation back to standard form?
3. Can you provide an example of a real-world application of scientific notation?
4. How would you express $0.0000000153$ in scientific notation?
5. What are the rules for adding or subtracting numbers expressed in scientific notation?

Tip: Always check the decimal point's position when converting between scientific notation and standard form!