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BRIDGE BACK
1. In the number 572, how is the value of 5 different from the value of 2?

2. Can you think of a situation where very large numbers are used? How does place value make these
numbers easier to read?

A number system is a way of representing numbers using specific digits or symbols. Each system
has a base (radix) that defines how numbers are written. Common systems are decimal, binary,
octal and hexadecimal.

DECIMAL NUMBER SYSTEM

The decimal number system is a base‑10 system that uses the digits 0–9. The value of each digit
depends on its position, which represents a power of 10. As you move from right to left, the place
value increases by powers of 10. This is the most commonly used number system in daily life.

The place value of each digit based on powers of 10 is shown below:

Digit Position Thousands Hundreds Tens Ones Tenths Hundredths

Position Value 3 2 1 0 –1 –2

n
–1
Weight (10 ) 10 3 10 2 10 1 10 0 10 ¹ 10 –2
For example: Consider the number 841

Place Hundreds Tens Ones

Place Value 10 2 10 1 10 0

Digit × Place Value 8 × 10 2 4 × 10 1 1 × 10 0

Expanded Form 800 40 1

So, the number 841 can be written as the sum: 841 = 800 + 40 + 1

BINARY NUMBER SYSTEM

The binary number system is a base‑2 system that uses only two digits: 0 and 1. Each digit, called
a bit, has a value depending on its position. The rightmost bit is the Least Significant Digit (LSD)
and the leftmost is the Most Significant Digit (MSD). Binary is used in computers and digital
devices, where 1 represents ON and 0 represents OFF.

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Number System