An astronomer wrote the distances in kilometers from Earth to two different stars in scientific notation:

- Distance from Earth to star A: [tex]2 \times 10^{13}[/tex]
- Distance from Earth to star B: [tex]8 \times 10^{15}[/tex]

About how many times farther from Earth is star B than star A?



Answer :

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.