To solve the given problem, we need to divide [tex]\(6.337 \times 10^4 \, m^2\)[/tex] by [tex]\(4.5136 \times 10^2 \, m\)[/tex]. Here is the detailed, step-by-step solution:
1. Identify the given values:
- Numerator: [tex]\(6.337 \times 10^4 \, m^2\)[/tex]
- Denominator: [tex]\(4.5136 \times 10^2 \, m\)[/tex]
2. Perform the division:
[tex]\[
\frac{6.337 \times 10^4}{4.5136 \times 10^2}
\][/tex]
3. Separate the scientific notation components:
[tex]\[
\left( \frac{6.337}{4.5136} \right) \times \left( \frac{10^4}{10^2} \right)
\][/tex]
4. Divide the coefficients:
[tex]\[
\frac{6.337}{4.5136} \approx 1.4040
\][/tex]
5. Divide the powers of 10:
[tex]\[
10^4 \div 10^2 = 10^{4-2} = 10^2
\][/tex]
6. Combine the results:
[tex]\[
1.4040 \times 10^2
\][/tex]
Thus, the quotient expressed in standard scientific notation with the appropriate number of significant figures is:
[tex]\[
1.4040 \times 10^2 \, \text{m}
\][/tex]
