To convert the given number [tex]\( 361.14 \times 10^8 \)[/tex] into correct scientific notation, follow these steps:
1. Identify the Current Form:
The number is [tex]\( 361.14 \times 10^8 \)[/tex].
2. Move the Decimal Point:
To express the coefficient in a form that meets scientific notation (a number between 1 and 10), move the decimal point two places to the left. This results in [tex]\( 3.6114 \)[/tex].
3. Adjust the Exponent:
Since we've moved the decimal point two places to the left, we must increase the exponent by 2 to balance the change. This is because moving the decimal point to the left requires an increment in the exponent to maintain the value of the number. Therefore, the new exponent becomes:
[tex]\[
8 + 2 = 10
\][/tex]
Putting it all together, the number [tex]\( 361.14 \times 10^8 \)[/tex] in correct scientific notation is:
[tex]\[
3.6114 \times 10^{10}
\][/tex]
Finally, placing the correct values into the boxes, we get:
- Coefficient (green box): 3.6114
- Exponent (yellow box): 10
