Multiplication patterns over increasing place values

Key notes:

🔹 Key Idea

When we multiply a number by 10, 100, 1,000, or higher powers of 10, the digits of the number shift to the left, and we add zeros at the end.

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🔹 Key Idea

Each digit moves one place to the left.

Example:

• 6 × 10 = 60
• 47 × 10 = 470

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🔹 Multiplying by 100

Each digit moves two places to the left.

Example:

• 6 × 100 = 600
• 47 × 100 = 4,700

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🔹 Multiplying by 1,000

Each digit moves three places to the left.

Example:

• 6 × 1,000 = 6,000
• 47 × 1,000 = 47,000

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🔹 Place Value Pattern

• Every time you multiply by 10, you add one zero to the number (if it is a whole number).
• Patterns Table:

Number	×10	×100	×1,000
3	30	300	3,000
15	150	1,500	15,000
247	2,470	24,700	247,000

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🔹 Rule

Multiplying by 10ⁿ shifts the digits n places to the left.

Example:

• 32 × 10 = 320 (1 place left)
• 32 × 100 = 3,200 (2 places left)
• 32 × 1,000 = 32,000 (3 places left)

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🔹 Word Problem Example

A pencil costs ₹25. What is the cost of 100 pencils?

• 25 × 100 = 2,500
• Answer: ₹2,500

A bus carries 47 passengers. How many passengers can 1,000 buses carry?

• 47 × 1,000 = 47,000
• Answer: 47,000 passengers

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Learn with an example

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