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A Peek Beyond the Point - Units of Measurement

Grade 7CBSE

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

🔑Concepts

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Decimal Place Value: The decimal point separates the whole number part from the fractional part. The positions to the right of the decimal point are tenths (110)(\frac{1}{10}), hundredths (1100)(\frac{1}{100}), and thousandths (11000)(\frac{1}{1000}).

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Metric System: The standard units of measurement use a base-10 system. Moving from a larger unit to a smaller unit involves multiplication by 1010, 100100, or 10001000. Moving from a smaller unit to a larger unit involves division.

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Length Conversion: The primary units are kilometres (kmkm), metres (mm), centimetres (cmcm), and millimetres (mmmm). For example, 1 m=100 cm1 \text{ m} = 100 \text{ cm}.

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Weight (Mass) Conversion: The primary units are kilograms (kgkg), grams (gg), and milligrams (mgmg). 1 kg=1000 g1 \text{ kg} = 1000 \text{ g}.

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Capacity Conversion: The primary units are litres (ll) and millilitres (mlml). 1 l=1000 ml1 \text{ l} = 1000 \text{ ml}.

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Money: In the Indian currency system, 100 paise=1 Rupee100 \text{ paise} = 1 \text{ Rupee}. Thus, 1 paisa=₹1100=₹0.011 \text{ paisa} = \text{₹} \frac{1}{100} = \text{₹} 0.01.

📐Formulae

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

1 m=100 cm1 \text{ m} = 100 \text{ cm}

1 cm=10 mm1 \text{ cm} = 10 \text{ mm}

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

1 g=1000 mg1 \text{ g} = 1000 \text{ mg}

1 litre=1000 ml1 \text{ litre} = 1000 \text{ ml}

Value in larger unit=Value in smaller unitConversion Factor\text{Value in larger unit} = \frac{\text{Value in smaller unit}}{\text{Conversion Factor}}

💡Examples

Problem 1:

Express 7575 paise as Rupees using decimals.

Solution:

₹0.75\text{₹} 0.75

Explanation:

Since 100 paise=1 Rupee100 \text{ paise} = 1 \text{ Rupee}, to convert paise to rupees, we divide by 100100. 75 paise=75100=₹0.7575 \text{ paise} = \frac{75}{100} = \text{₹} 0.75.

Problem 2:

Convert 5 km 25 m5 \text{ km } 25 \text{ m} into kilometres.

Solution:

5.025 km5.025 \text{ km}

Explanation:

We know 1000 m=1 km1000 \text{ m} = 1 \text{ km}. Therefore, 1 m=11000 km1 \text{ m} = \frac{1}{1000} \text{ km}. Converting 25 m25 \text{ m} gives 251000 km=0.025 km\frac{25}{1000} \text{ km} = 0.025 \text{ km}. Adding this to the 5 km5 \text{ km}, we get 5+0.025=5.025 km5 + 0.025 = 5.025 \text{ km}.

Problem 3:

Subtract $3.456  kg\text{ kg} from 8.000 kg8.000 \text{ kg} using vertical subtraction.

Solution:

8.000−3.4564.544\begin{array}{r} 8.000 \\ - 3.456 \\ \hline 4.544 \end{array}

Explanation:

To subtract decimals, align the decimal points vertically. Borrow from the whole number places to subtract the thousandths, hundredths, and tenths places. 8.000−3.456=4.544 kg8.000 - 3.456 = 4.544 \text{ kg}.

Problem 4:

A bottle contains 1.5 litres1.5 \text{ litres} of juice. How many millilitres is this?

Solution:

1500 ml1500 \text{ ml}

Explanation:

To convert from litres to millilitres, we multiply by 10001000 because 1 l=1000 ml1 \text{ l} = 1000 \text{ ml}. 1.5×1000=1500 ml1.5 \times 1000 = 1500 \text{ ml}.