Final answer:
To find the maximum distance of the space probe from the sun on a scale model, convert the real distance from kilometers to meters and then apply the scale factor of 1 billion. The resulting maximum scaled distance is 1.95 x 10¹⁴ meters.
Step-by-step explanation:
The question asks us to calculate the maximum distance of the space probe from the sun on a scaled-down model, with the real distance being 1.9 x 10¹° kilometers, which is correct to 2 significant figures.
To convert this distance into meters for the scale model, we first convert kilometers to meters by multiplying by 10³ (since 1 km equals 1000 meters). Then, we apply the scale factor of 1 billion (10¹) to reduce the actual distance for the model.
Step 1: Convert kilometers to meters
1.9 x 10¹° km x 10³ m/km = 1.9 x 10¹³ meters
Step 2: Apply the scale factor
1.9 x 10¹³ m / (10¹ scaling factor) = 1.9 x 10¹⁴ meters
Since the question asks for the maximum distance, we need to consider that the given distance (1.9 x 10¹° km) is correct to 2 significant figures, so the maximum distance could be up to 1.95 x 10¹° km (due to rounding). Following the same conversion process:
1.95 x 10¹° km x 10³ m/km = 1.95 x 10¹³ meters
Then applying the scale factor to find the maximum distance on the scale model:
1.95 x 10¹³ m / (10¹ scaling factor) = 1.95 x 10¹⁴ meters
Therefore, the maximum distance of the space probe from the sun on the scale model would be 1.95 x 10¹⁴ meters.