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Converting centimeters to millimeters with a scale factor is simple! Just follow these steps:

1. First, multiply the given value by 10 to convert centimeters to millimeters.
2. Then, divide the result by the scale factor.

Example: Let’s say you have 50 cm and a scale factor of 1:5.

• Convert 50 cm to mm → 50 × 10 = 500 mm
• Apply the scale factor 1:5 → 500 ÷ 5 = 100 mm

So, the final scaled measurement is 100 mm.

A 1:100 scale means that 1 unit on the model is equal to 100 units in real life.

For example, if you are designing a building floor plan and a wall measures 2 cm on the drawing at a 1:100 scale, the actual wall size in real life would be:

2 cm × 100 = 200 cm (or 2 meters).

Similarly, if a desk is 0.5 inches on the model, its real-world size would be:

0.5 × 100 = 50 inches (or about 4.2 feet).

This scale is commonly used in architectural drawings and maps to represent large objects in a compact and easy-to-read format.

Other related scales:
1:50 (used for larger architectural plans)
1:25 (used for furniture and detailed layouts)
1:100 (used for building layouts and site plans)

The formula to calculate the scale factor is:

Scale Factor=Dimensions of the new shapeDimensions of the original shape\text{Scale Factor} = \frac{\text{Dimensions of the new shape}}{\text{Dimensions of the original shape}}Scale Factor=Dimensions of the original shapeDimensions of the new shape​

Example 1: Scaling Down

If an original room is 500 cm long and you want to draw it at a 1:50 scale, the drawing size would be:

500÷50=10 cm500 \div 50 = 10 \text{ cm}500÷50=10 cm

So, a 500 cm room would be 10 cm in the scaled drawing.

Example 2: Scaling Up

If a model car is 20 cm and the actual car is 400 cm, the scale factor is:

400÷20=1:20400 \div 20 = 1:20400÷20=1:20

This means the real car is 20 times larger than the model.

The scale factor helps adjust measurements accurately when creating drawings, models, or resizing objects.

The conversion formula depends on the units you are converting between. Here are some common methods:

1. General Unit Conversion Formula:

Converted Value=(Original Value×Conversion FactorScale Factor)\text{Converted Value} = \left( \frac{\text{Original Value} \times \text{Conversion Factor}}{\text{Scale Factor}} \right)Converted Value=(Scale FactorOriginal Value×Conversion Factor​)

Example: Convert 500 millimeters to meters using a conversion factor of 1,000 mm = 1 m and a scale factor of 1:5:

(500×1)÷(1000×5)=0.1 meters(500 \times 1) \div (1000 \times 5) = 0.1 \text{ meters}(500×1)÷(1000×5)=0.1 meters

1. Two-Step Conversion with Scale Factor:

Final Value=(Original Value×First Scale FactorSecond Scale Factor)\text{Final Value} = \left( \frac{\text{Original Value} \times \text{First Scale Factor}}{\text{Second Scale Factor}} \right)Final Value=(Second Scale FactorOriginal Value×First Scale Factor​)

Example: Convert 200 cm to mm, using a scale factor of 1:10 first, and then a scale factor of 1:2:

1. 1. Convert cm to mm: 200×10=2000 mm200 \times 10 = 2000 \text{ mm}200×10=2000 mm
   2. Apply first scale factor: 2000÷10=200 mm2000 \div 10 = 200 \text{ mm}2000÷10=200 mm
   3. Apply second scale factor: 200×2=400 mm200 \times 2 = 400 \text{ mm}200×2=400 mm

So, the final converted value is 400 mm.