Conversion of a Pure Recurring Decimal to the Form p/q | question and answer !

Question:-

Conversion of a Pure Recurring Decimal to the Form p/q

Answer:-

In a non-terminating repeating decimal, there are two types of decimal representations.

(i) A decimal in which all the digits after the decimal point are repeated. These types of decimals are known as pure recurring decimals.

For example: 0.6, 0.16, 0.123 are pure recurring decimals.

(ii) A decimal in which at least one of the digits after the decimal point is not repeated and then some digit or digits are repeated. This type of decimals are known as mixed recurring decimals.

For example: 2.16, 0.35, 0.785 are mixed recurring decimals.

In order to convert a pure recurring decimal to the form p/q, we follow the following steps.

STEP 1 - Obtain the repeating decimal and put it equal to x (say).

STEP 11 - Write the number in decimal from by removing bar from the top of repeating digits and listing repeating digits at least twice.
For expamle: - write x = 0.8 as x = 0.888..... and x = 0.14 as x = 0.141414..........

STEP 111 - Determine the number of digits having bar on their heads.

STEP 1V - If the repeating decimal has 1 place repetition, multiply by 10: a two place repetition, multiply by 100: a three place repetition, multiply by 1000 and so on.

STEP V - Subtract the number in step 11 form the number obtained in step 1V.

STEP V1 - Divide both side of the equation by the coefficient of x.

STEP V11 - Write the rational number in its simplest form.