Conversion of Terminating Decimals to Rational Numbers||Terminating vs Non Terminating Representaion

Terminating Decimals

A terminating decimal that has an ends. It is a decimal, which has a finite number of digits(or terms) in the quotient when the numerator of the Rational number is divided by the denominator of the rational number.

Eg. 0.15, 0.86 etc.

Non-Terminating Decimals

A non-terminating decimals are the one that do not have an end term. It has infinite number of terms in the quotient when the numerator of the Rational number is divided by the denominator of the rational number.

Eg. 0.5444444….., 0.1111111….., etc.

Repeating and Non-Repeating decimals

Repeating decimals are the one, which have a set of terms in a decimal to be repeated in a uniform manner i.e. a fixed pattern is being repeated infinite number of times in the quotient when the numerator of the Rational number is divided by the denominator of the rational number.

Eg. 0.666666…., 0.123123…., etc.

It is to be noted that the repeated term in a decimal are represented by bar on top of the repeated part. Such as 0.333333…..=0.3¯.

Whereas non-repeating decimals are the one that do have have repeated terms.

Non-Terminating and non-repeating decimals are said to be an Irrational number. Eg. √2=1.4142135…….

The square roots of all the terms (leaving perfect squares) are irrational numbers.

Non- Terminating and repeating decimals are Rational Numbers and can be represented in the form of p/q, where q is not equal to 0.