To convert the number [tex]\( 38.7 \times 10^7 \)[/tex] into correct scientific notation, we should ensure that the number is represented in the form [tex]\( [\text{coefficient}] \times 10^{[\text{exponent}]} \)[/tex], where the coefficient is a number greater than or equal to 1 and less than 10.
1. Identify the coefficient:
We start with 38.7. To express this in scientific notation correctly, the coefficient should be a number between 1 and 10. Hence, we move the decimal point one place to the left, which changes 38.7 to 3.87.
2. Adjust the exponent:
Since we moved the decimal point one place to the left, we need to increase the exponent by 1. Initially, the exponent was 7. Moving the decimal one place left makes the exponential term [tex]\( 10^8 \)[/tex] (since [tex]\( 10^7 \times 10^1 = 10^8 \)[/tex]).
Putting these together, we get the number [tex]\( 38.7 \times 10^7 \)[/tex] expressed in scientific notation as [tex]\( 3.87 \times 10^8 \)[/tex].
So,
- The coefficient is [tex]\( 3.87 \)[/tex] (to be entered in the green box).
- The exponent is [tex]\( 8 \)[/tex] (to be entered in the yellow box).
Thus, the final scientific notation is:
[tex]\[
3.87 \times 10^8
\][/tex]
