a) To calculate the distance travelled by the Earth in one day:
The circumference of the Earth’s orbit is:
\( 2 \times \pi \times 150000000 \)

Distance travelled in one day (out of 365 days):
\( \frac{2 \times \pi \times 150000000}{365} \)

Calculate:
\( \pi \approx 3.1415926535 \)
\( 2 \times \pi \times 150000000 \approx 942477796.076 \)
\( \frac{942477796.076}{365} \approx 2582129.851 \)

To 3 significant figures:
\( 2580000 \, \text{km} \)

Thus:
Distance travelled is \( 2580000 \, \text{km} \) [4]

b) To express the answer from part (a) in the form \( a \times 10^k \):
From part (a), the distance is \( 2580000 \, \text{km} \).
Convert to scientific notation:
\( 2580000 = 2.58 \times 10^6 \)

Here, \( a = 2.58 \), \( k = 6 \), satisfying \( 1 \leqslant a \leqslant 10 \) and \( k \in \mathbb{Z} \).

Thus:
\( 2.58 \times 10^6 \, \text{km} \) [2]