Decimal Fraction

Let you have a fraction a ⁄ b, where "a", "b" are numbers and b ≠ 0.

If b = 10, 100, 1000 ... (i.e. denominator equals any power of ten with cardinal exponent), this case the fraction is called "decimal fraction".

You may write any decimal fraction by two ways.

Example:

You see, any decimal fraction is a fraction, so you may do addition, multiplication, division ... with decimal fractions as with fractions.
But, if a decimal fraction is written as a decimal number, you have to do addition, multiplication, division ... by special ways. There are the special rules for decimal numbers.

Example:

1,3 × 2 = 2,6
20,84 ÷ 10 = 2,084
7,05 + 11,1 = 18,15

It's interesting!

It doesn't matter what form (decimal fraction or decimal number) you choose for doing addition, subtraction, division ... You know: "Tastes differ". But, sure you have to do these operations by the rules and certainly correctly.

On the other hand, not every fraction may be changed into a decimal one. Let you have two numbers: a decimal number and a fraction (can't be written as a decimal one), then the decimal number must be changed into a decimal fraction for doing any mathematical operation.
Read more about decimal fractions, do sums with them, and you'll see: "The proof of the pudding is in the eating".