convert into rational 22.1009090909_____
Answers
Answer:
Case I: When the decimal number is of terminating nature.
Algorithm:
Step-1: Obtain the rational number.
Step-2: Determine the number of digits in its decimal part.
Step-3: Remove decimal point from the numerator. Write 1 in the denominator and put as many zeros on the right side of 1 as the number of digits in the decimal part of the given rational number.
Step-4: Find a common divisor of the numerator and denominator and express the rational number to lowest terms by dividing its numerator and denominator by the common divisor.
Case II: When decimal representation is of non-terminating repeating nature.
In a non terminating repeating decimal, there are two types of decimal representations
A decimal in which all the digit after the decimal point are repeated. These type of decimals are known as pure recurring decimals.
For Example: 0.6¯¯¯,0.16¯¯¯¯¯,0.123¯¯¯¯¯¯¯¯ are pure recurring decimals.
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.