To convert the given number into scientific notation, we follow these steps:
1. Identify the given number and exponent:
[tex]\[
78.3 \times 10^{11}
\][/tex]
2. Understand the format of scientific notation:
Scientific notation is expressed as:
[tex]\[
a \times 10^b
\][/tex]
where [tex]\(a\)[/tex] is a number such that [tex]\(1 \leq a < 10\)[/tex], and [tex]\(b\)[/tex] is an integer.
3. Express the given number in the form [tex]\(a \times 10^b\)[/tex]:
The numeral part of the given number is 78.3. To express 78.3 as a number between 1 and 10, identify how to rewrite it:
[tex]\[
78.3 = 7.83 \times 10^1
\][/tex]
4. Combine the exponents properly:
Multiply the exponential parts based on the laws of exponents:
[tex]\[
78.3 \times 10^{11} = (7.83 \times 10^1) \times 10^{11}
\][/tex]
Using the laws of exponents ([tex]\(10^a \times 10^b = 10^{a+b}\)[/tex]):
[tex]\[
(7.83 \times 10^1) \times 10^{11} = 7.83 \times 10^{1+11} = 7.83 \times 10^{12}
\][/tex]
5. Write the final answer in correct scientific notation:
[tex]\[
78.3 \times 10^{11} = 7.83 \times 10^{12}
\][/tex]
Thus, the number [tex]\(78.3 \times 10^{11}\)[/tex] in scientific notation is:
[tex]\[
7.83 \times 10^{12}
\][/tex]
