Certainly! To convert [tex]\(38.7 \times 10^7\)[/tex] into its correct scientific notation, follow these steps:
1. Identify the Initial Parameters:
- Coefficient: 38.7
- Exponent: 7
2. Adjust the Coefficient:
- Scientific notation requires the coefficient to be a number between 1 and 10.
- To adjust 38.7 so it's between 1 and 10, divide it by 10. As a result, 38.7 becomes 3.87.
3. Adjust the Exponent:
- Since we divided the coefficient by 10, we need to balance this change in the exponent.
- Subtracting an exponent is equivalent to dividing by 10. Thus, we should add 1 to the exponent to balance it.
- Hence, the original exponent 7 increases by 1, resulting in 8.
4. Combine the Results:
- The new coefficient is 3.87.
- The new exponent is 8.
- Therefore, [tex]\(38.7 \times 10^7\)[/tex] is correctly expressed as [tex]\(3.87 \times 10^8\)[/tex].
Thus, the scientific notation for [tex]\(38.7 \times 10^7\)[/tex] is:
[tex]\[ \boxed{3.87} \times 10^{\boxed{8}} \][/tex]
Feel free to enter 3.87 in the green box and 8 in the yellow box.
