Number 2
5 marks · HardThe distance from the Earth to Star X is 2.46 × 10^{12} km. The distance from the Earth to Star Y is 7.82 × 10^{13} km.
Calculate how many times farther Star Y is from Earth compared to Star X. Give your answer in standard form.
If a spaceship travels at 2.05 × 10^{5} km per hour, estimate how many hours it would take to reach Star X from Earth. Give your answer in standard form.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
(a) 3.18 × 10^{1}
(b) 1.20 × 10^{7} hours
Common mistakes: Incorrectly dividing or multiplying the powers of ten; Ignoring multiplication rules for a×10^n
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Attempts to divide the two distances in standard form: (7.82 × 10^{13}) ÷ (2.46 × 10^{12})
A1 (a) · 2 marks · Correct answer in standard form: 3.18 × 10^{1} (accept 31.8), with working.
M2 (b) · 1 mark · Attempts to divide the distance to Star X by the speed, using correct standard form rules.
A2 (b) · 1 mark · Correct answer (1.20 × 10^{7}) in standard form with working.
Worked solution
a) To find how many times farther Star Y is from Earth compared to Star X:
Star Y is 3.18 × 10^{1} (or 31.8) times farther from Earth than Star X.
b) To estimate the travel time to Star X: