Decimal Representation of Rational Numbers

Decimal Representation of Rational Numbers

Points to be Remember:-

1.   If in a rational number numerator is a natural number and 

     denominator is power of 10 like 10, 100, 1000 etc., then to 

     represent such rational number in decimal form. We count the

     number of zeros just coming after one in denominator and we 

     put decimal in numerator after leaving same number of digit

     from right side to left side.

2.   The rational number whose denominator is a power of 2 or 5 or both like, 2, 4, 8, 16 ……, or 5, 25, 125 …. Then its denominator is changed into the power of 10 by multiplying with a suitable number and then it can be written in decimal form.

3.   The rational number whose denominator is not a power o 10 or it is not possible to write denominator in such form, then numerator is divided by denominator to represent rational number in the decimal form. After dividing upto unit place of numerator we put decimal after one’s place and divide by putting zeros after decimal.

4.   While changing the rational number to its decimal form by division method, if the remainder obtained is zero then the decimal number is known as terminating decimal or a rational number whose denominator contains powers of 2 or 5 or both, can be represented as a terminating decimal.

5.   While changing the rational number to its decimal form by division method, if the division process does not come o any and i.e., we get number (other then zero) as remainder then decimal number so obtained is known as non-terminating decimal.

6.   To change terminating decimal to rational number following steps are followed:

Step 1:  Write the given number

Step 2:  Count the number of digits after decimal in given number.

Step 3: Remove decimal from the decimal number and take all the  

            digits as numerator. Now after one put zeros which are in 

            number equal to the number of digits on the right side of 

            decimal and take it as denominator.

Step 4:  Find H.C.F. of numerator and denominator. Divide numerator

              and denominator by H.C.F. to find the rational number in 

              simplest form.