Answer: To determine if a number is written in scientific notation, we look for two key elements: a coefficient and a power of 10.
Let's analyze each number given and determine if it is written in scientific notation:
1. 13.8 x 10^-3: Yes, this number is written in scientific notation because it has a coefficient (13.8) and a power of 10 (-3).
2. 3.098 x 10^12: Yes, this number is written in scientific notation because it has a coefficient (3.098) and a power of 10 (12).
3. 0.57 x 10^-2: Yes, this number is written in scientific notation because it has a coefficient (0.57) and a power of 10 (-2).
4. 2.91 x 10^-6: Yes, this number is written in scientific notation because it has a coefficient (2.91) and a power of 10 (-6).
Now, let's analyze the numbers that are not written in scientific notation:
1. 0.096 x 10^5: This number is not written in scientific notation because the coefficient (0.096) is less than 1. In scientific notation, the coefficient should be between 1 and 10.
2. 7.0 x 10^-4: This number is not written in scientific notation because the coefficient (7.0) is not expressed as a single digit followed by a decimal. In scientific notation, the coefficient should be expressed as a single digit before the decimal point.
To summarize, the numbers written in scientific notation are: 13.8 x 10^-3, 3.098 x 10^12, 0.57 x 10^-2, and 2.91 x 10^-6. The numbers not written in scientific notation are: 0.096 x 10^5 and 7.0 x 10^-4.
Explanation: