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A decimal number can be defined as a number whose whole number part and the fractional part is separated by a decimal point. The dot in a decimal number is called a decimal point The digits following the decimal point show a value smaller than one.
Decimal Numbers can be classified as
In the above diagram, Rational Numbers are:
And Irrational Numbers are Non-terminating non-repeating (non-recurring) decimal numbers. (This we will discuss in upcoming concepts.)
Note:
Terminating decimal: Now if we convert fractions to decimals. Remember that the fraction bar indicates division. So can be written 4÷5. This means that we can convert a fraction to a decimal by treating it as a division problem.
Example:
Solution:
Here 8 can be re-written as
In this a finite number of digit occurs after the decimal.
Non-terminating repeating (recurring) decimal numbers:
So far, in all the examples converting fractions to decimals, the division resulted in a remainder of zero. This is not always the case. Let’s see what happens when we convert the fraction to a decimal.
Example:
Solution:
Here 11 cannot be written in the form of
The remainder never becomes zero.
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