Write down this radius, in kilometres, in the form \(a \times {10^k}\), where \(1 \leqslant a < 10,{\text{ }}k \in \mathbb{Z}\).

The Earth travels around the Sun in one orbit. It takes one year for the Earth to complete one orbit.

Calculate the distance, in kilometres, the Earth travels around the Sun in one orbit, assuming that the orbit is a circle.

Today is Anna’s 17th birthday.

Calculate the total distance that Anna has travelled around the Sun, since she was born.

\(1.5 \times {10^8}{\text{ (km)}}\)     (A2)     (C2)

Notes: Award (A2) for the correct answer.

     Award (A1)(A0) for 1.5 and an incorrect index.

     Award (A0)(A0) for answers of the form \(15 \times {10^7}\).

[2 marks]

\(2\pi 1.5 \times {10^8}\)     (M1)

\( = 942\,000\,000{\text{ (km)   (942}}\,{\text{477}}\,{\text{796.1}} \ldots {\text{, }}3 \times {10^8}\pi ,{\text{ }}9.42 \times {10^8})\)     (A1)(ft)     (C2)

Notes: Award (M1) for correct substitution into correct formula. Follow through from part (a).

     Do not accept calculator notation \(9.42{\text{E}}8\).

     Do not accept use of \(\frac{{22}}{7}\) or\( 3.14\) for \(\pi\).

[2 marks]

\(17 \times 942\,000\,000\)     (M1)

\( = 1.60 \times {10^{10}}{\text{ (km) }}\left( {{\text{1.60221}} \ldots  \times {{10}^{10}}{\text{, 1.6014}} \times {{10}^{10}},{\text{ 16}}\,{\text{022}}\,{\text{122}}\,{\text{530, }}(5.1 \times {{10}^9})\pi } \right)\)     (A1)(ft)     (C2)

Note: Follow through from part (b).

[2 marks]