What Are Decimals?

You already use decimals every day — when you check the temperature (36.6°C), pay for something ($4.99), or measure your height (1.52 m). Decimals are simply a way of representing numbers that fall between whole numbers.

Decimal

A number that uses a decimal point to separate the whole-number part from the fractional part. For example, in 3.75, the whole-number part is 3 and the fractional part is .75.

The decimal system is based on powers of 10. Each place in a decimal number is worth 10 times more than the place to its right, and 10 times less than the place to its left. This is the same pattern you already know from whole numbers — decimals just extend it to the right of the decimal point.

Analogy

Think of a decimal number like money. In $12.35, the 1 represents ten dollars, the 2 represents single dollars, the 3 represents tenths of a dollar (dimes), and the 5 represents hundredths of a dollar (cents). Each column is 10 times smaller as you move right.

Decimal Place Value

Every digit in a decimal number has a specific place value. Let's look at the number 4 627.385 to understand each position:

Place	Thousands	Hundreds	Tens	Ones	.	Tenths	Hundredths	Thousandths
Value	1 000	100	10	1	.	$\frac{1}{10}$	$\frac{1}{100}$	$\frac{1}{1000}$
Digit	4	6	2	7	.	3	8	5

So in 4 627.385:

The 4 is worth $4 \times 1000 = 4000$
The 6 is worth $6 \times 100 = 600$
The 2 is worth $2 \times 10 = 20$
The 7 is worth $7 \times 1 = 7$
The 3 is worth $3 \times 0.1 = 0.3$
The 8 is worth $8 \times 0.01 = 0.08$
The 5 is worth $5 \times 0.001 = 0.005$

Place Value

The value of a digit based on its position in a number. Moving left, each place is 10 times larger. Moving right, each place is 10 times smaller.

Exam Tip

A quick way to remember the decimal places: Tenths, Hundredths, Thousandths — they mirror the whole-number places (Tens, Hundreds, Thousands) but with a "-ths" ending.

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