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Write down the difference between bar scale and number scale. Explain the meaning of the scale 1:50. Calculate the actual length of the desk in metres.

Mathematics

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3.1.1 Write down the difference between bar scale and number scale.

  • A bar scale is a visual representation of the scale, typically a line marked with divisions that show actual distances. It remains accurate even if the plan is enlarged or reduced.
  • A number scale (or ratio scale) is expressed as a ratio (e.g., 1:50) or a fraction. It indicates the ratio of a distance on the plan to the actual distance, but it becomes inaccurate if the plan is enlarged or reduced without recalculating.

3.1.2 Explain the meaning of the scale 1:50.
The scale 1:50 means that 1 unit of measurement on the plan represents 50 units of the same measurement in actual reality. For example, 1 centimeter on the plan corresponds to an actual distance of 50 centimeters.

3.1.3 Calculate the actual length of the desk in metres.

  1. Use the given plan length and scale to find the actual length in centimeters.

    Plan length of desk =6 cm= 6 \text{ cm}
    Scale =1:50= 1:50

    Actual length in cm=Plan length×Scale factor\text{Actual length in cm} = \text{Plan length} \times \text{Scale factor} Actual length in cm=6 cm×50=300 cm\text{Actual length in cm} = 6 \text{ cm} \times 50 = 300 \text{ cm}

  2. Convert the actual length from centimeters to meters.

    1 m=100 cm1 \text{ m} = 100 \text{ cm} Actual length in m=300 cm100 cm/m=3 m\text{Actual length in m} = \frac{300 \text{ cm}}{100 \text{ cm/m}} = 3 \text{ m}

    The actual length of the desk is 3 m\boxed{\text{3 m}}.

    3.1.4 Calculate the actual distance between the desks in metres.

  3. Use the given plan distance and scale to find the actual distance in centimeters.

    Plan distance between desks =4 cm= 4 \text{ cm}
    Scale =1:50= 1:50

    Actual distance in cm=Plan distance×Scale factor\text{Actual distance in cm} = \text{Plan distance} \times \text{Scale factor} Actual distance in cm=4 cm×50=200 cm\text{Actual distance in cm} = 4 \text{ cm} \times 50 = 200 \text{ cm}

  4. Convert the actual distance from centimeters to meters.

    1 m=100 cm1 \text{ m} = 100 \text{ cm} Actual distance in m=200 cm100 cm/m=2 m\text{Actual distance in m} = \frac{200 \text{ cm}}{100 \text{ cm/m}} = 2 \text{ m}

    The actual distance between the desks is 2 m\boxed{\text{2 m}}.

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