To solve the problem [tex]\(\frac{1}{2.67 \times 10^{11}}\)[/tex] and express the answer in scientific notation with 2 decimal places, we follow these steps:
1. Understand the Division: We need to divide the number 1 by [tex]\(2.67 \times 10^{11}\)[/tex]. This is essentially finding how many times [tex]\(2.67 \times 10^{11}\)[/tex] fits into 1.
2. Perform the Division:
[tex]\[
\frac{1}{2.67 \times 10^{11}}
\][/tex]
Conceptually, this division operation will result in a very small number because the numerator (1) is much smaller compared to the denominator ([tex]\(2.67 \times 10^{11}\)[/tex]).
3. Calculate the Result: When we divide 1 by [tex]\(2.67 \times 10^{11}\)[/tex], we obtain a result of approximately:
[tex]\[
3.745318352059925 \times 10^{-12}
\][/tex]
4. Express in Scientific Notation:
To express this result in scientific notation with 2 decimal places, we need to round the number [tex]\(3.745318352059925\times 10^{-12}\)[/tex] to two decimal places.
- Look at the digits beyond the second decimal place (which are [tex]\(5318352059925\)[/tex] in this case).
- If the digit immediately after the second decimal place (which is 5 here) is 5 or more, we round up the second decimal place.
Using this rounding procedure, [tex]\(3.745318352059925 \times 10^{-12}\)[/tex] rounds to:
[tex]\[
3.75 \times 10^{-12}
\][/tex]
5. Final Answer:
Therefore, the result of [tex]\(\frac{1}{2.67 \times 10^{11}}\)[/tex] when expressed in scientific notation with 2 decimal places is:
[tex]\[
3.75 \times 10^{-12}
\][/tex]
Thus, the final answer is [tex]\(3.75 \times 10^{-12}\)[/tex].
