To convert the number [tex]\(78.3 \times 10^{11}\)[/tex] into correct scientific notation, we need to express the number in the form [tex]\(a \times 10^b\)[/tex] where [tex]\(1 \le a < 10\)[/tex].
Let's break it down step-by-step:
1. Identify the given number:
It is [tex]\(78.3 \times 10^{11}\)[/tex].
2. Locate the coefficient and the exponent:
The coefficient is initially 78.3, and the exponent is 11.
3. Adjust the coefficient to meet the scientific notation criteria:
Scientific notation requires that the coefficient be in the range of [tex]\(1 \le a < 10\)[/tex].
- Currently, the coefficient is 78.3, which is greater than 10.
4. Modify the coefficient and adjust the exponent:
- If we change 78.3 to a number between 1 and 10, we need to move the decimal place one position to the left.
- Moving the decimal place one position to the left means we divide 78.3 by 10 to get 7.83.
- To balance that division, we need to increase the exponent by 1.
Thus:
- Dividing 78.3 by 10 gives us 7.83.
- Increasing the exponent by 1 alters [tex]\(10^{11}\)[/tex] to [tex]\(10^{12}\)[/tex].
So, the number [tex]\(78.3 \times 10^{11}\)[/tex] in scientific notation is:
[tex]\[ 7.83 \times 10^{12} \][/tex]
In summary, the coefficient (green box) is:
[tex]\[ \boxed{7.83} \][/tex]
And the exponent (yellow box) is:
[tex]\[ \boxed{12} \][/tex]
