# How do we Write a Non Terminating Recurring Decimal in the form P by Q? Part 1 | Don't Memorise | Summary and Q&A

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December 18, 2014
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Infinity Learn NEET
How do we Write a Non Terminating Recurring Decimal in the form P by Q? Part 1 | Don't Memorise

## TL;DR

Learn how to convert non-terminating recurring decimals to the form P by Q by eliminating the recurring decimal through equations.

## Key Insights

• 💁 Equating a recurring decimal to a variable, multiplying by 10, and subtracting equations allows for the elimination of the recurring decimal and conversion to P by Q form.
• 😥 Mixed recurring decimals require manipulating equations to have only the recurring part after the decimal point for successful conversion.
• 😑 The process of converting non-terminating recurring decimals involves shifting digits, subtracting equations, and simplifying expressions.
• 💁 The aim is to eliminate the recurring decimal and achieve a rational number in P by Q form.
• 👻 Understanding the steps to convert non-terminating recurring decimals allows for easy conversion of such decimals into fractions.
• 😥 Multiplying equations by appropriate powers of 10 helps in aligning the recurring part after the decimal point for efficient subtraction.
• ✊ The process of converting mixed recurring decimals involves extra steps, such as multiplying equations by powers of 10, to obtain the desired form.

## Transcript

how do we convert a non-terminating recurring decimal to the form P by Q take the number 0.3 with a bar over three how do we get this in the form P by Q it's simple but in interesting let's equate x with 0.3 bar you will know soon as to why we're doing this a bar over 3 means X = 0.3333 and so on let this be our first equation there's only one way ... Read More

### Q: How do you convert a non-terminating recurring decimal to P by Q form?

Start by equating the recurring decimal to a variable and multiplying both sides by 10 to eliminate the recurring part. Subtract the equations to remove the recurring decimal, and simplify the resulting expression to obtain the fraction in P by Q form.

### Q: What is the purpose of multiplying both sides of the equation by 10?

Multiplying by 10 helps eliminate the recurring decimal by shifting all the digits to the left, making them easier to subtract in the following step.

### Q: How do you convert a mixed recurring decimal to P by Q form?

Multiply the equation with just the recurring part by an appropriate power of 10 to obtain a second equation with the recurring part after the decimal. Subtracting these equations allows for the elimination of the recurring decimal and the conversion to the desired rational number form.

### Q: What is the importance of having equations with just the recurring part after the decimal point?

By having equations with only the recurring part, subtracting them eliminates the recurring part while leaving behind the non-recurring part, resulting in the conversion to rational number form.

## Summary & Key Takeaways

• To convert a non-terminating recurring decimal to P by Q form, equate the decimal to a variable and multiply both sides by 10 to eliminate the recurring decimal.

• Subtracting the equations with and without the recurring decimal allows for its elimination, resulting in a rational number.

• For mixed recurring decimals, aim to have equations with just the recurring part after the decimal point and subtract them to eliminate the recurring decimal.