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Proportional Reasoning-1 - Unit Conversions

Grade 8CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Unit conversion involves expressing a quantity measured in one unit into an equivalent value in another unit using a conversion factor.

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A conversion factor is a ratio that expresses how many of one unit are equal to another unit (e.g., 1 km=1000 m1 \text{ km} = 1000 \text{ m}).

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To convert from a larger unit to a smaller unit (e.g., kmkm to mm), we multiply the value by the conversion factor.

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To convert from a smaller unit to a larger unit (e.g., gg to kgkg), we divide the value by the conversion factor.

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Proportional reasoning can be used by setting up a ratio: Unit AUnit B=Given Value AUnknown Value B\frac{\text{Unit A}}{\text{Unit B}} = \frac{\text{Given Value A}}{\text{Unknown Value B}}.

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Square units (Area) and Cubic units (Volume) require the conversion factor to be squared or cubed respectively. For example, since 1 m=100 cm1 \text{ m} = 100 \text{ cm}, then 1 m2=(100)2 cm2=10,000 cm21 \text{ m}^2 = (100)^2 \text{ cm}^2 = 10,000 \text{ cm}^2.

📐Formulae

1 km=1000 m1 \text{ km} = 1000 \text{ m}

1 m=100 cm=1000 mm1 \text{ m} = 100 \text{ cm} = 1000 \text{ mm}

1 kg=1000 g1 \text{ kg} = 1000 \text{ g}

1 L=1000 mL=1000 cm31 \text{ L} = 1000 \text{ mL} = 1000 \text{ cm}^3

1 hour=60 minutes=3600 seconds1 \text{ hour} = 60 \text{ minutes} = 3600 \text{ seconds}

1 km/h=1000 m3600 s=518 m/s1 \text{ km/h} = \frac{1000 \text{ m}}{3600 \text{ s}} = \frac{5}{18} \text{ m/s}

Value in New Unit=Value in Old Unit×Conversion Factor\text{Value in New Unit} = \text{Value in Old Unit} \times \text{Conversion Factor}

💡Examples

Problem 1:

Convert 5.4 km5.4 \text{ km} into meters.

Solution:

We know that 1 km=1000 m1 \text{ km} = 1000 \text{ m}. To convert from a larger unit (kmkm) to a smaller unit (mm), we multiply: 5.4×1000=5400 m5.4 \times 1000 = 5400 \text{ m}

Explanation:

Since 11 kilometer contains 10001000 meters, 5.45.4 kilometers will contain 5.45.4 times 10001000 meters.

Problem 2:

Convert 750 grams750 \text{ grams} into kilograms.

Solution:

We know that 1000 g=1 kg1000 \text{ g} = 1 \text{ kg}. To convert from a smaller unit (gg) to a larger unit (kgkg), we divide: 7501000=0.75 kg\frac{750}{1000} = 0.75 \text{ kg}

Explanation:

Divide the mass in grams by 10001000 because there are 10001000 grams in every 11 kilogram.

Problem 3:

A car is traveling at a speed of 90 km/h90 \text{ km/h}. Express this speed in m/s\text{m/s}.

Solution:

Using the conversion factor 1 km/h=518 m/s1 \text{ km/h} = \frac{5}{18} \text{ m/s}: 90×518=5×5=25 m/s90 \times \frac{5}{18} = 5 \times 5 = 25 \text{ m/s}

Explanation:

To convert speed from km/hkm/h to m/sm/s, we multiply by the fraction 10003600\frac{1000}{3600}, which simplifies to 518\frac{5}{18}.

Problem 4:

Convert 2 m22 \text{ m}^2 into cm2\text{cm}^2.

Solution:

Since 1 m=100 cm1 \text{ m} = 100 \text{ cm}, then: 1 m2=100 cm×100 cm=10,000 cm21 \text{ m}^2 = 100 \text{ cm} \times 100 \text{ cm} = 10,000 \text{ cm}^2 Therefore, 2 m2=2×10,000=20,000 cm22 \text{ m}^2 = 2 \times 10,000 = 20,000 \text{ cm}^2

Explanation:

For area conversions, the linear conversion factor must be applied twice (once for length and once for width).