Decimals
Decimal Basics – Understanding Decimal Numbers
A decimal is a way of writing numbers that are not whole. The decimal point separates the whole part of a number from the part that is less than one. Decimals are used every single day — in prices, measurements, temperatures, and scores.
Decimal notation as we know it was popularised in Europe by the Flemish mathematician Simon Stevin in his 1585 pamphlet De Thiende (“The Tenth”), which argued that merchants, surveyors, and everyone else doing arithmetic should abandon clumsy fractions in favour of base-10 decimal notation. The dot notation itself was popularised slightly later, championed by mathematicians such as John Napier in the early 1600s. Before decimals became standard, most calculations in trade and science relied on ordinary fractions or, in the Babylonian tradition, base-60 place value — decimals were a genuine efficiency breakthrough.
Where Do Decimals Come From?
You already know that 1/2 means half of something. A decimal gives us another way to write that same value: 0.5. Both mean exactly the same thing — half.
The Decimal Point
The dot in a decimal number is called the decimal point. Everything to its left is a whole number. Everything to its right is less than one whole.
Example: 34.76
34 is the whole part.
.76 is the decimal part — less than one whole.
Reading Decimals
| Number | How to Read It |
|---|---|
| 0.3 | Zero point three |
| 1.5 | One point five |
| 4.72 | Four point seven two |
| 0.08 | Zero point zero eight |
| 12.005 | Twelve point zero zero five |
Decimals in Everyday Life
- Prices: a loaf of bread costs £1.49
- Measurements: a door is 2.05 m tall
- Temperature: body temperature is 37.5°C
- Sport: a race is won in 9.58 seconds
- Weight: a bag of apples weighs 1.25 kg
The Link Between Decimals and Fractions
| Fraction | Decimal | Meaning |
|---|---|---|
| 1/10 | 0.1 | One tenth |
| 1/100 | 0.01 | One hundredth |
| 1/4 | 0.25 | Twenty-five hundredths |
| 1/2 | 0.5 | Five tenths |
| 3/4 | 0.75 | Seventy-five hundredths |
Zeros After the Decimal Point
Adding zeros at the end of a decimal does not change its value. 0.5 = 0.50 = 0.500. They are all the same. But zeros between the decimal point and other digits DO matter. 0.05 is different from 0.5 — it is ten times smaller.
Key Takeaways
- Decimals are just another way to write fractions and mixed numbers.
- The decimal point separates the whole part from the fractional part.
- Trailing zeros after the last non-zero digit do not change the value.
- Zeros between the decimal point and a digit do change the value.