We see decimals everywhere around us on price tags, bank interest rates, temperature etc. All the quantities cannot be expressed using whole numbers. Hence, we use a special number systemcalled decimal number system that allows us to write any quantity using a special symbol “.”

‘Decimal’ means based on ten. We can use either fractions or decimals to represent part of a whole. But decimals are particularly used to represent fractions that have 10 or 100 or 1000 or other multiples of 10 as their denominators. Here is a model of decimal numbers.

The first model shows one whole where all the squares are shaded. The second model shows one tenth and the third, one hundredth.

The fractions whose denominators are tens or multiples of ten are called as the Decimal Fractions. Example, $\frac{3}{10}$, $\frac{6}{100}$. They can easily be written in the form of decimal numbers.

The fraction $\frac{7}{10}$ is written in decimal form as 0.7

The fraction $\frac{7}{100}$ is written as 0.07 in decimal form.

Decimal number has two parts, whole number part and decimal part.The decimal point separates the whole number from the fractional part of the number. The number that is to the left of the decimal point are whole numbers and those to the right of decimal point are called as “tenths”. For example, 12.35, 12 is the whole number part and there is a point that separates it from the fractional part 35 out of 100. This number is read as “Twelve point three five” or “Twelve and thirty five hundredths”.

When we say \$3.99, it means 3 dollars and 0.99 is a part of the dollar. It is 99/100. That is $3 and 99 cents!

We can locate the decimal numbers on a number line.

## Examples

**Example: Locate 1.24 on a number line.**

**Solution: **

**Example: Write the number represented by the picture shown below.**

**Solution:** The scale shows three and seven tenths. That is **3.7**

The decimals can be written as fractions and fractions as decimals. To convert a fraction into a decimal we just have to divide the numerator by the denominator. The farther right a number is from the decimal point, the lesser is its value. It is useful to remember a few of the decimal values like,

¼ = 0.25, ½ = 0.5, ¾ = 0.75

When a proper fraction is converted into decimal form, the whole number part is zero. When an improper fraction or a mixed number is converted into decimal form, then the whole number is non zero.

We can order, add, subtract, multiply and also divide the decimal numbers! Decimal system of numbers are based on multiples and submultiples of ten.

Note: Adding one or more zeroes to the right end of decimal number after the decimal point does not change its value. Example, 2.34 = 2.3400