For this purpose, we will have to multiply the original number by ‘100’. Step IV: Now we would require moving the repeating digits to the left of the decimal point in the original decimal number. This can be accomplished by multiplying the given number by’10,000’. To do so, we are required to move the decimal point to the right by 4 places. Step III: Now have to place the repeating digits ‘78’ to the left of the decimal point. Step II: After analyzing the expression, we identified that the repeating digits are ‘78’. into a rational fraction.Ĭonverting the given decimal number into a rational fraction can be performed by undertaking the following conversion steps: X = 124.4/99 = 1244/990 = 622/495 Example of Conversion of Repeating Decimal to FractionĬonvert the numerical digit 4.567878…. Therefore, x = 7/9 is the required rational number.Įxample: Convert 1.256 (two recurring digit) into a fraction Solve for x, expressing the answer as the fraction in the simplest form Subtracting (1) from (3) to remove the recurring part Solution: Follow the below steps to convert Recurring Decimals to fractions: Solved ExamplesĮxample: Convert 0.7 (one recurring digit) into a fraction. As we subtract, just ensure the differences of both sides will be positive. Then, do the subtraction on the right side of the two equations. Step V: Now deduct the left sides of the two equations. Step IV: Place the repeating digits to the right of the decimal point. Step III: Carefully place the repeating digits to the left of the decimal point. Step II: observe the Repeating Decimal to identify the repeating digits. Step I: Let ‘x’ be the Repeating Decimal number that we want to convert into a rational number. Let’s check the steps involved in converting Repeating Decimals to fractions recurring (rational). Let us understand and perform an example to understand how we a Recurring Decimal to a fraction. It forms part of their basic Mathematical aptitude in various competitive exams in the future. These numbers are known as irrational numbers and cannot be written in the form of a fraction.Ĭonverting Recurring Decimals to FractionsĬonversion of Recurring Decimals into fractions is very useful for students throughout their academic life and also thereafter. Irrational: These Decimals go on forever, are never-ending and also never form a repeating pattern. Recurring Decimals: These consist of one or more repeating numbers or sequences of numbers followed by the decimal point, which keeps on infinitely.įor example, 5.232323…., 21.123123…, 0.1111…. Terminating Decimals: these decimals have a finite number of digits followed by the decimal point. When performing the conversion from fractions to decimals, you can formulate whether the decimal will terminate or recur.ĭecimal numbers are classified into three types i.e.: They are also called non-terminating decimals and non-Repeating Decimal numbers. Non - recurring numbers are those in Mathematics that do not repeat their values after a decimal point. To display a repeating digit in a decimal number, often we put a dot or a line over the repeating digit as shown below:ġ/3=0.33333.=0. These numbers are also called Repeating Decimals. Recurring Decimal numbers are those numbers that keep on repeating the same value after a decimal point. To solve such problems first, you need to know what Repeating Decimal is. Have you ever come across decimal numbers and wondered why not all such numbers have a fixed number of digits after the decimal point? Or how do I convert these numbers into fractions? These are some questions that keep students bothered for a long time. A recurring decimal exists when decimal numbers repeat forever.
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