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Author: Admin | 2025-04-27
Written By Rachana Last Modified 22-06-2023 Terminating and Non-Terminating Decimals: The decimal numbers are used to express both whole numbers and fractions. Depending on the type of digits after the decimal point, decimals can be categorised into several types such as repeating, non-repeating, ending, or un-ending (infinite digits after the decimal point). There are two types of decimals they are terminating and non-terminating decimals.A terminating decimal is a decimal number with a finite number of digits after the decimal point. A non-terminating decimal will never end but may predictably repeat one or more values after the decimal point. Scroll down to know what is terminating decimal, what is non-terminating decimals, repeating decimals and more. Terminating and Non-Terminating Decimals DefinitionWhat is Terminating Decimal: Numbers with a fixed or finite number of digits following the decimal point are known as terminating decimals. In the same way that fractions represent the partial amount of a whole, decimal numbers represent a whole.Example: \(0.2,\,0.125\) and \(0.35\)These terminating decimals can be expressed in the form \(\frac{p}{q}.\)Example: Express \(0.2\) in the form of \(\frac{p}{q}.\)Solution: \(0.2 = \frac{{0.2 \times 10}}{{10}} = \frac{2}{{10}} = \frac{1}{5}\)Non-terminating Decimal Definition: A non-terminating decimal has infinite decimal places. The digits after the decimal point will not terminate. A non-terminating decimal can be repeating or non-repeating. A non-terminating, non-repeating decimal is a decimal number with no repeating digits and continues indefinitely. The non-terminating and non-recurring or non-repeating decimals are irrational numbers. Because it’s an irrational number, this decimal can’t be stated as a fraction.When we split a fraction expressed in decimal form, we receive any remainder. The decimal is non-terminating if the dividing technique does not result in a remainder equal to zero. In some circumstances, a single digit or a group of digits in the decimal component repeats. A sort of non-terminating repeating decimal is pure repeated decimals, which are also known as non-terminating repeating decimals. To symbolize these decimal numbers, a bar is put on the replicated portion.Example: \(0.2857142857\) and \(0.3333….. = 0.\overline 3 \)There are two forms of non-terminating decimal expansions, they are:(i) Non-terminating recurring decimal expansion(ii) Non-terminating non-recurring decimal expansionNon-Terminating Repeating Decimal ExpansionA non-terminating decimal is a decimal with an infinite number of digits after the decimal point.A non-terminating, recurring decimal is a decimal in which some digits after the decimal point repeat without terminating. A non-terminating, recurring decimal can be expressed as \(\frac{p}{q}\) form.Example: \(0.666….\) or \(0.\overline 6 ,\,2.6666…\) or \(2.\overline 6 .\)Express \(0.\overline 6 \) in the form of \(\frac{p}{q}\)Here, \(0.\overline 6 = 0.6666…\)Take, \(x = 0.6666…\)\(10\,x = 6.6666…\) (Multiplying \(10\) on both sides)\( \Rightarrow 10\,x = 6 + 0.6666…\)\( \Rightarrow 10\,x = 6 + x…\) \(∵\left( {x = 0.666…} \right)\)\( \Rightarrow 10\,x – x = 6\)\( \Rightarrow
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