To determine which number is written in scientific notation, we need to follow the rules for scientific notation:
1. The coefficient (the number before the multiplication sign) must be a number between 1 and 10.
2. The coefficient must be multiplied by 10 raised to some power (positive or negative).
Let's examine each option step by step:
### Option 1: [tex]\(4.5 \times 10^{-3}\)[/tex]
1. The coefficient is 4.5, which is between 1 and 10.
2. The exponent is -3, and it is a power of 10.
Since both conditions are satisfied, this number is written in scientific notation.
### Option 2: [tex]\(14.5 \times 10^2\)[/tex]
1. The coefficient is 14.5, which is not between 1 and 10.
This does not satisfy the first condition, so this number is not written in scientific notation.
### Option 3: [tex]\(0.78 \times 10^{-6}\)[/tex]
1. The coefficient is 0.78, which is not between 1 and 10.
This does not satisfy the first condition, so this number is not written in scientific notation.
### Option 4: [tex]\(5.7 \times 4^8\)[/tex]
1. The coefficient is 5.7, which is between 1 and 10.
2. However, the exponent base is 4, not 10.
This does not satisfy the second condition, so this number is not written in scientific notation.
### Conclusion
Only Option 1 ([tex]\(4.5 \times 10^{-3}\)[/tex]) meets all the criteria for scientific notation. Therefore, the number that is written in scientific notation is:
[tex]\[ \boxed{4.5 \times 10^{-3}} \][/tex]
