Convert 0.6 Repeating To A Fraction Easily

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Converting a repeating decimal to a fraction can be a bit tricky, but don't worry, I'm here to guide you through the process.

What is 0.6 Repeating?

0.6 repeating, also known as 0.666..., is a decimal number that goes on forever with the digit 6 repeating. This type of decimal is called a repeating decimal.

Why Convert 0.6 Repeating to a Fraction?

Converting a repeating decimal to a fraction can be helpful in various mathematical operations, such as adding, subtracting, multiplying, and dividing fractions. It's also useful in algebra, geometry, and other branches of mathematics.

Step-by-Step Conversion

To convert 0.6 repeating to a fraction, follow these easy steps:

1. Let x be the repeating decimal: Let x = 0.666...
2. Multiply x by 10: Multiply both sides of the equation by 10 to get 10x = 6.666...
3. Subtract the original equation: Subtract the original equation (x = 0.666...) from the new equation (10x = 6.666...) to get 9x = 6.
4. Solve for x: Divide both sides of the equation by 9 to get x = 6/9.
5. Simplify the fraction: Simplify the fraction 6/9 to its lowest terms, which is 2/3.

Conclusion

And that's it! You've successfully converted 0.6 repeating to a fraction, which is 2/3. This process can be applied to any repeating decimal to convert it to a fraction. Just remember to multiply by a power of 10, subtract the original equation, and simplify the resulting fraction.

Additional Tips

• When converting a repeating decimal to a fraction, make sure to multiply by a power of 10 that is equal to the number of repeating digits.
• Always simplify the resulting fraction to its lowest terms to ensure accuracy.

Now, go ahead and try converting other repeating decimals to fractions using this easy method!

Gallery of Repeating Decimals

FAQs

I hope you found this article helpful! If you have any questions or need further clarification, feel free to ask in the comments section.