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Airthmatic Operations on Decimals for CLAT - Practice Questions & MCQ

Edited By admin | Updated on Oct 05, 2023 05:01 PM | #CLAT

Concepts Covered - 1

Airthmatic Operations on Decimals

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 q=2^n\cdot5^n where n is any whole number then we will get Terminating Decimal Numbers
  • If q\neq2^n\cdot5^n 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 \frac45 can be written 4÷5. This means that we can convert a fraction to a decimal by treating it as a division problem.

Example: \frac18

Solution:

Here 8 can be re-written as 8=2^3\cdot5^0

\frac18=0.125

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 \frac2{11} to a decimal.
Example: \frac2{11}

Solution: 

Here 11 cannot be written in the form of 2^n\cdot5^n

\frac2{11}=0.181818\ldots=0.\overline{18}

The remainder never becomes zero.

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