Decimals Explained

What is a decimal?

A decimal is a way of writing numbers that are not whole. The decimal point separates the whole part from the part smaller than one.

In 3.74:

• 3 is the whole number part.
• .74 is the part less than one.

Decimals let us be precise about money, measurements and scores: $3.74, 1.5 metres, or a time of 9.58 seconds.

Decimal place value

Just like whole numbers have tens and hundreds, the digits after the point have their own places. Each place to the right is ten times smaller than the one before.

Place	Tens	Ones	•	Tenths	Hundredths	Thousandths
Value	10	1	•	0.1	0.01	0.001
Example 12.345	1	2	•	3	4	5

So in 12.345, the 3 means 3 tenths, the 4 means 4 hundredths, and the 5 means 5 thousandths.

Reading decimals

Read the whole part normally, say "point", then read each digit:

• 0.7 → "zero point seven" (7 tenths)
• 4.25 → "four point two five" (4 and 25 hundredths)

Decimals and fractions

A decimal is just another way to write a fraction with a denominator of 10, 100 or 1000.

Decimal	Fraction	In words
0.5	5/10 = 1/2	one half
0.25	25/100 = 1/4	one quarter
0.75	75/100 = 3/4	three quarters

If you want a refresher on the fraction side, see introduction to fractions.

Comparing decimals

To compare decimals, line up the decimal points and compare digit by digit from the left. It helps to add zeros so each number has the same number of decimal places.

Compare 0.4 and 0.39:

• Write them as 0.40 and 0.39.
• Tenths: 4 vs 3 → 4 is bigger.

So 0.4 > 0.39, even though 0.39 has more digits.

Adding and subtracting decimals

The golden rule: line up the decimal points, then add or subtract as usual.

Worked example: 2.6 + 1.45

  2.60
+ 1.45
------
  4.05

We rewrote 2.6 as 2.60 so both numbers had two decimal places. The answer is 4.05.

Worked example: 5.3 − 2.18

  5.30
- 2.18
------
  3.12

The answer is 3.12.

Rounding decimals

To round to a certain number of decimal places, look at the next digit:

• If it is 5 or more, round up.
• If it is 4 or less, round down (keep the digit the same).

Round 5.367 to one decimal place. The second decimal digit is 6 (which is 5 or more), so the tenths digit rounds up: 5.367 → 5.4.

Why decimals matter

Decimals appear everywhere: prices, distances, temperatures and times. Once you understand place value, the rest is just lining up points carefully. To go further, link decimals to percentages and ratios you will meet in algebra basics.