To solve the problem of expressing [tex]\(\left(1.8 \times 10^{-2}\right) \div \left(9 \times 10^2\right)\)[/tex] in scientific notation with the same number of significant figures as the starting value, let's follow these steps:
1. Identify the given values:
- Numerator: [tex]\(1.8 \times 10^{-2}\)[/tex]
- Denominator: [tex]\(9 \times 10^2\)[/tex]
2. Perform the division of the coefficients:
- Divide the coefficient of the numerator by the coefficient of the denominator:
[tex]\[
\frac{1.8}{9} = 0.2
\][/tex]
3. Handle the powers of ten:
- Subtract the exponent of the denominator from the exponent of the numerator:
[tex]\[
10^{-2} \div 10^2 = 10^{-2 - 2} = 10^{-4}
\][/tex]
4. Combine the results:
- Coefficient from step 2: [tex]\(0.2\)[/tex]
- Power of ten from step 3: [tex]\(10^{-4}\)[/tex]
- Combined result:
[tex]\[
0.2 \times 10^{-4}
\][/tex]
5. Convert the result into proper scientific notation:
- Convert [tex]\(0.2 \times 10^{-4}\)[/tex] to [tex]\(2.0 \times 10^{-5}\)[/tex]. This conversion ensures the answer has the same number of significant figures (1.8 has 2 significant figures).
Therefore, the final answer, expressed in scientific notation with the same number of significant figures as the starting value, is:
[tex]\[
2.0 \times 10^{-5}
\][/tex]
