Identify the type of scale for A, B, C, and D, and confirm if A and D are the same type. Convert C to a ratio scale.

Based on the previous context and the definitions of scale types:

• A: $1 : 50\,000$ is a Ratio scale (or Numerical scale).
• B: A bar scale is a Graphic scale (or Bar scale).
• C: $1 \text{ cm} = 2,5 \text{ km}$ is a Verbal scale (or Statement scale).
• D: $1 : 200$ is a Ratio scale (or Numerical scale).

$$\boxed{\text{1.2 A: Ratio scale}}$$ $$\boxed{\text{1.2 B: Graphic scale}}$$ $$\boxed{\text{1.2 C: Verbal scale}}$$ $$\boxed{\text{1.2 D: Ratio scale}}$$

The learner claims that Scale A ($1 : 50\,000$) and Scale D ($1 : 200$) are the same type of scale. Both are expressed as numerical ratios.

• Agreement: Yes, I agree.
• Reason: Both Scale A and Scale D are ratio scales (also known as numerical scales or representative fractions) because they express the relationship between map distance and ground distance as a fraction or ratio.

$$\boxed{\text{1.3 Yes, I agree. Both Scale A and Scale D are ratio scales, expressing the relationship between map distance and ground distance as a numerical ratio.}}$$

To convert a verbal scale to a ratio scale, both sides of the equation must be in the same units.
We know that $1 \text{ km} = 1000 \text{ m}$ and $1 \text{ m} = 100 \text{ cm}$.
Therefore, $1 \text{ km} = 1000 \times 100 \text{ cm} = 100\,000 \text{ cm}$.

Now, convert $2,5 \text{ km}$ to centimeters:

$$2,5 \text{ km} = 2,5 \times 100\,000 \text{ cm} = 250\,000 \text{ cm}$$

So, the verbal scale $1 \text{ cm} = 2,5 \text{ km}$ becomes $1 \text{ cm} = 250\,000 \text{ cm}$.
The ratio scale is $1 : 250\,000$.

$$\text{Working:}$$ $$1 \text{ cm} = 2,5 \text{ km}$$ $$1 \text{ km} = 100\,000 \text{ cm}$$ $$2,5 \text{ km} = 2,5 \times 100\,000 \text{ cm}$$ $$2,5 \text{ km} = 250\,000 \text{ cm}$$ $$\text{Therefore, } 1 \text{ cm} = 250\,000 \text{ cm}$$ $$\boxed{\text{1.4 Answer: Scale C as a ratio = } 1 : 250\,000}$$

$1 : 50\,000$) and a 'large-scale map' (Scale D: $1 : 200$) in terms of detail.

• A small-scale map (like $1 : 50\,000$) has a small representative fraction (e.g., $\frac{1}{50\,000}$). This means a small unit on the map represents a large distance on the ground. Consequently, it covers a large geographical area but shows less detail.
• A large-scale map (like $1 : 200$) has a large representative fraction (e.g., $\frac{1}{200}$). This means a small unit on the map represents a small distance on the ground. Consequently, it covers a small geographical area but shows more detail, such as individual buildings or specific features.

$$\boxed{\text{1.5 A small-scale map (e.g., } 1 : 50\,000 \text{) covers a large geographical area but shows less detail. A large-scale map (e.g., } 1 : 200 \text{) covers a small geographical area but shows more detail.}}$$