Metric System Chapter Notes | Mathematics Class 5 ICSE PDF Download

Introduction

Imagine measuring the world around you with a universal language that everyone understands! The metric system is like a magic ruler that helps us measure length, weight, and capacity in a simple and organized way. From tiny millimeters to vast kilometers, from light grams to heavy kilograms, and from small milliliters to large liters, this system makes measurements easy and fun. In this chapter, we'll explore how to use different units, convert them, and solve everyday problems with confidence!

Metric System

• Measurements use standard units in the metric system.
• Standard unit for length is the metre (m).
• Standard unit for weight is the gram (g).
• Standard unit for capacity is the litre (L).
• Larger and smaller units are created by adding prefixes to these standard units.
• Prefixes indicate how big or small a unit is compared to the standard unit.

Example: The table below shows different units for measuring length, weight, and capacity:

Prefixes in the Metric System

• Prefixes like kilo, hecto, deca, deci, centi, and milli are added to standard units.
• Each prefix has a specific meaning and value showing how big or small the unit is.
• Kilo means thousand (1,000).
• Hecto means hundred (100).
• Deca means ten (10).
• Deci means one-tenth (1/10).
• Centi means one-hundredth (1/100).
• Milli means one-thousandth (1/1000).

Example: The table below shows the meaning and value of prefixes:

Conversion of Metric Measures

Length

• Length measures things like height, distance, or size of objects.
• Small objects can be measured using a ruler with centimetre (cm) and millimetre (mm) markings.
• Each small division on a ruler is 1 millimetre (mm).
• To convert from a larger unit to a smaller unit, multiply by 10 for each step down.
• To convert from a smaller unit to a larger unit, divide by 10 (or multiply by 1/10) for each step up.

Example: Convert 5 hm to dm.

• Step 1: 1 hm = 1,000 dm (since hm to dm involves three steps: , multiply by 10 × 10 × 10 = 1,000).
• Step 2: 5 hm = 5 × 1,000 dm = 5,000 dm.
  So, 5 hm = 5,000 dm.

Expressing Length in Decimal Form

• Converting smaller units to larger units can be expressed as decimals.
• 1 m = 100 cm, so 1 cm = 1/100 m = 0.01 m.
• 1 km = 1,000 m, so 1 m = 1/1000 km = 0.001 km.
• Decimal point separates the larger unit (like km) from smaller units (like hm, dam, m).

Example: Express 14 km 6 hm 3 dam 7 m in km using decimal notation.

• Step 1: Convert each unit to km.
  6 hm = 6/10 km = 0.6 km (1 hm = 1/10 km).
  3 dam = 3/100 km = 0.03 km (1 dam = 1/100 km).
  7 m = 7/1000 km = 0.007 km (1 m = 1/1000 km).
• Step 2: Add all parts: 14 km + 0.6 km + 0.03 km + 0.007 km = 14.637 km.
  So, 14 km 6 hm 3 dam 7 m = 14.637 km.

Weight

• Weight has a standard unit of gram (g).
• Convert larger units to smaller units by multiplying by 10 for each step down.
• Convert smaller units to larger units by dividing by 10 for each step up.

Example: Convert 4 hg to dg.

• Step 1: 1 hg = 1,000 dg (since hg to dg involves three steps:, multiply by 10 × 10 × 10 = 1,000).
• Step 2: 4 hg = 4 × 1,000 dg = 4,000 dg.
  So, 4 hg = 4,000 dg.

Expressing Weight in Decimal Form

• Weights can be expressed as decimals when converting to larger units.
• 1 kg = 1,000 g, so 1 g = 1/1000 kg = 0.001 kg.
• 1 g = 1,000 mg, so 1 mg = 1/1000 g = 0.001 g.

Example: Express 7 kg 3 hg 2 dag 7 g in kg using decimal notation.

• Step 1: Convert each unit to kg.
  3 hg = 3/10 kg = 0.3 kg (1 hg = 1/10 kg).
  2 dag = 2/100 kg = 0.02 kg (1 dag = 1/100 kg).
  7 g = 7/1000 kg = 0.007 kg (1 g = 1/1000 kg).
• Step 2: Add all parts: 7 kg + 0.3 kg + 0.02 kg + 0.007 kg = 7.327 kg.
  So, 7 kg 3 hg 2 dag 7 g = 7.327 kg.

Capacity

• Capacity has a standard unit of litre (L).
• Convert larger units to smaller units by multiplying by 10 for each step down.
• Convert smaller units to larger units by dividing by 10 for each step up.

Example: Convert 8 L 3 daL to L.

• Step 1: 1 daL = 10 L.
• Step 2: 3 daL = 3 × 10 L = 30 L.
• Step 3: Add: 8 L + 30 L = 38 L.
  So, 8 L 3 daL = 38 L.

Expressing Capacity in Decimal Form

• Capacities can be expressed as decimals when converting to larger units.
• 1 L = 1,000 mL, so 1 mL = 1/1000 L = 0.001 L.
• 1 kL = 1,000 L, so 1 L = 1/1000 kL = 0.001 kL.

Example: Express 6,214 L in kL using decimal notation.

• Step 1: 1 L = 1/1000 kL.
• Step 2: 6,214 L = 6,214 ÷ 1,000 kL = 6.214 kL.
  So, 6,214 L = 6.214 kL.

Four Basic Operations on Metric Measures

• Metric measures can be added, subtracted, multiplied, or divided after converting to decimal form.
• Convert all measures to the same unit before performing operations.
• Place the decimal point correctly in the result for multiplication and division.

Addition

• Convert all measures to the same unit using decimal notation.
• Add the decimal numbers as usual.

Example: Add 5 km 3 hm 7 dam 9 m, 4 km 6 hm 1 m, and 2 hm 8 m.

• Step 1: Convert to km using decimal notation.
  5 km 3 hm 7 dam 9 m = 5 + 0.3 + 0.07 + 0.009 = 5.379 km.
  4 km 6 hm 1 m = 4 + 0.6 + 0.001 = 4.601 km.
  2 hm 8 m = 0.2 + 0.008 = 0.208 km.
• Step 2: Add: 5.379 km + 4.601 km + 0.208 km = 10.188 km.
  So, the sum is 10.188 km.

Subtraction

• Convert all measures to the same unit using decimal notation.
• Subtract the decimal numbers as usual.

Example: Subtract 32 m 82 cm from 84 m 67 cm and express in metres.

• Step 1: Convert to metres.
  84 m 67 cm = 84 + 0.67 = 84.67 m.
  32 m 82 cm = 32 + 0.82 = 32.82 m.
• Step 2: Subtract: 84.67 m - 32.82 m = 51.85 m.
  So, the difference is 51.85 m.

Multiplication

• Convert the measure to decimal form in the required unit.
• Multiply as with whole numbers, ensuring the decimal point is placed correctly.

Example: Multiply 38 kg 500 g by 24.

• Step 1: Convert to kg: 38 kg 500 g = 38 + 0.5 = 38.5 kg.
• Step 2: Multiply: 38.5 × 24 = 924 kg.
  So, the product is 924 kg.

Division

• Convert the measure to decimal form in the required unit.
• Divide as with whole numbers, placing the decimal point correctly in the quotient.

Example: Divide 98 kL 928 L by 54 and express in litres.

• Step 1: Convert to kL: 98 kL 928 L = 98 + 0.928 = 98.928 kL.
• Step 2: Divide: 98.928 ÷ 54 = 1.832 kL.
• Step 3: Convert to L: 1.832 kL = 1.832 × 1,000 = 1,832 L.
  So, the quotient is 1,832 L.

Word Problems on Metric Measures

• Word problems involve applying addition, subtraction, multiplication, or division to solve real-life situations.
• Convert all measures to the same unit before calculating.
• Ensure the answer is in the unit asked for in the problem.

Example: Pari made fruit cream using 500 g apples, 600 g grapes, 450 g pomegranates, and 250 g bananas. How much fruit did she use?

• Step 1: Convert to kg.
  Apples: 500 g = 0.5 kg.
  Grapes: 600 g = 0.6 kg.
  Pomegranates: 450 g = 0.45 kg.
  Bananas: 250 g = 0.25 kg.
• Step 2: Add: 0.5 + 0.6 + 0.45 + 0.25 = 1.80 kg.
  So, Pari used 1.80 kg of fruits.