Base 10 Positional Number System

The number system we use every day is called the Base Ten Positional Number System. It is based on ten digits and the position of each digit gives it value.

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1. Digits

The symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 are called digits.

Using these 10 digits, we can form any number by placing them in different positions.

Important: Only 10 digits create all numbers in mathematics.

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2. Why It Is Called Base Ten

Our system is called Base Ten because:

• It uses 10 digits (0–9).
• Each place value is 10 times the place to its right.

Place	Value
Ones	1
Tens	10
Hundreds	100
Thousands	1000

Rule: Moving from right to left, each position becomes 10 times bigger.

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3. Positional Value (Very Important)

In a positional system, the value of a digit depends on its position.

Example: 345

• 5 is in the ones place → value = 5
• 4 is in the tens place → value = 40
• 3 is in the hundreds place → value = 300

345 = 300 + 40 + 5

The same digit can have different values depending on its position.

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4. Commas

When numbers have more than three digits, commas are used to make them easy to read.

• 1000 → 1,000
• 1000000 → 1,000,000

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5. Periods

Each group of three digits separated by commas is called a period.

Example: 1,234,567

• 567 → Ones Period
• 234 → Thousands Period
• 1 → Millions Period

Each period has three positions:

• Ones
• Tens
• Hundreds

This pattern repeats for every new period.

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6. Period Names (Up to Trillions)

Period	Example
Ones	567
Thousands	234,000
Millions	1,000,000
Billions	1,000,000,000
Trillions	1,000,000,000,000

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Final Key Concept

In the Base Ten Positional Number System, the value of a digit is determined by its position in the number.