Sure, let's solve the division of two numbers expressed in scientific notation step by step.
We are given the expression:
[tex]\[
(3.6 \times 10^{-5}) \div (1.8 \times 10^2)
\][/tex]
We can rewrite the division of the numbers in scientific notation. When we divide numbers in scientific notation, we can handle the coefficients and the powers of 10 separately:
[tex]\[
\frac{3.6 \times 10^{-5}}{1.8 \times 10^2}
\][/tex]
Separate the coefficients (3.6 and 1.8) and the powers of 10:
[tex]\[
\frac{3.6}{1.8} \times \frac{10^{-5}}{10^2}
\][/tex]
Calculate the division of the coefficients:
[tex]\[
\frac{3.6}{1.8} = 2
\][/tex]
Next, use the quotient rule for exponents to divide the powers of ten:
[tex]\[
\frac{10^{-5}}{10^2} = 10^{-5 - 2} = 10^{-7}
\][/tex]
Therefore, combining the results we get:
[tex]\[
2 \times 10^{-7}
\][/tex]
In standard form, we write this as:
[tex]\[
2.00 \times 10^{-7}
\][/tex]
So, the result of [tex]\( \left(3.6 \times 10^{-5}\right) \div \left(1.8 \times 10^2\right) \)[/tex], in standard form, is:
[tex]\[
2.00 \times 10^{-7}
\][/tex]
