Certainly! To determine how many times farther star B is from Earth compared to star A, you need to compare the distances by performing a division of the distances given for each star. Here’s a step-by-step solution:
1. Express the distances in standard form (though it's not necessary for the calculation, it helps to understand the size of the numbers):
- Distance from Earth to star A: [tex]\( 2 \times 10^{13} \)[/tex] kilometers, which is [tex]\( 20,000,000,000,000 \)[/tex] kilometers.
- Distance from Earth to star B: [tex]\( 8 \times 10^{15} \)[/tex] kilometers, which is [tex]\( 8,000,000,000,000,000 \)[/tex] kilometers.
2. Set up the division to find how many times farther star B is than star A:
[tex]\[
\frac{\text{Distance to star B}}{\text{Distance to star A}} = \frac{8 \times 10^{15}}{2 \times 10^{13}}
\][/tex]
3. Simplify the expression:
[tex]\[
\frac{8}{2} \times \frac{10^{15}}{10^{13}}
\][/tex]
4. Divide the coefficients (the numbers in front of the exponential notation):
[tex]\[
\frac{8}{2} = 4
\][/tex]
5. Subtract the exponents of the powers of 10 (since [tex]\(10^{a} / 10^{b} = 10^{a-b}\)[/tex]):
[tex]\[
10^{15} / 10^{13} = 10^{15-13} = 10^{2}
\][/tex]
6. Combine the simplified parts:
[tex]\[
4 \times 10^{2} = 4 \times 100 = 400
\][/tex]
Conclusion:
Star B is approximately 400 times farther from Earth than star A. This provides a clear understanding that star B is significantly farther away compared to star A by a factor of 400.
