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To determine which numbers are written in scientific notation, let's recall that a number is in scientific notation if it is written as:

\[
a \times 10^n
\]
where \(1 \leq |a| < 10\) and \(n\) is an integer.

### Analysis of the options:

1. **\(12 \times 10^6\)**: This is not in scientific notation because the coefficient \(12\) is greater than 10.
2. **\(12\)**: This is a standard number and not written in scientific notation.
3. **\(6.89 \times 10^6\)**: This is in proper scientific notation since \(6.89\) is between 1 and 10.
4. **\(6.89\)**: This is not written in scientific notation, as it lacks the "× 10^n" part.
5. **\(0.4\)**: This is not written in scientific notation.
6. **\(4 \times 10^{-1}\)**: This is not in scientific notation because although it's in the form \(a \times 10^n\), \(4\) is not strictly between 1 and 10 (the lower bound includes 1, but not smaller numbers).

### Conclusion
The only number in scientific notation here is **\(6.89 \times 10^6\)**.

Would you like further details or explanations?

### Additional Questions
1. Why is \(4 \times 10^{-1}\) not considered proper scientific notation?
2. How would you convert \(12 \times 10^6\) into proper scientific notation?
3. What is the purpose of scientific notation, and when is it most commonly used?
4. How would you convert a number like 0.0045 into scientific notation?
5. How can you tell if a number is too large or too small to be conveniently expressed without scientific notation?

### Tip
Always check that the coefficient \(a\) in scientific notation is between 1 and 10 (inclusive of 1 but not 10) to ensure the expression is correctly formatted.

Which of the following numbers are written in scientific notation?

Learn how to identify which numbers are written in scientific notation. This problem covers core concepts of exponents and scientific notation, perfect for students in Grades 7-9.

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