Tiling a Square Floor — Count of 50 cm Tiles: A square room of side 10 m is to be fully tiled with square tiles of side 50 cm. What is the smallest number of tiles needed?

Introduction / Context:
Counting tiles requires dividing the floor area by the area of one tile, keeping units consistent. Here, dimensions mix metres and centimetres, so converting to the same unit avoids mistakes.

Given Data / Assumptions:

• Room: square, side = 10 m
• Tile: square, side = 50 cm = 0.5 m
• No wastage assumed; exact tiling

Concept / Approach:
Room area = 10 * 10 = 100 m^2. Tile area = 0.5 * 0.5 = 0.25 m^2. Number of tiles = 100 / 0.25 = 400. This is a simple area division once units are aligned in metres.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 200 and 300 undercount; 500 and 600 overcount.

Common Pitfalls:

• Leaving tile side in centimetres and mixing units.

Final Answer:
400.