CAT Discussing Decimals - Practice Questions & MCQ

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:

1. Terminating decimal numbers and
2. Non-terminating repeating (recurring) decimal numbers.

And Irrational Numbers are Non-terminating non-repeating (non-recurring) decimal numbers. (This we will discuss in upcoming concepts.)

Note: 

• If  where n is any whole number then we will get Terminating Decimal Numbers
• If  where n is any whole number then we will get Non-Terminating Repeating Decimal Numbers

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.