How to Convert Decimals To Fractions - Math trick for recurring decimals | Summary and Q&A

TL;DR

Learn how to convert repeating decimals to fractions using a simple and efficient method.

Key Insights

• 🔁 Converting repeating decimals to fractions involves representing the repeating digits with a line over them.
• #️⃣ Multiplying the equation by a number with zeros equal to the number of repeating digits helps align the decimals.
• 👻 Subtracting one equation from the other eliminates the repeating pattern and allows us to solve for the fraction.
• 🧑‍🏭 The resulting fraction can be simplified by finding a common factor for the numerator and denominator.
• 🔁 There are patterns in converting specific repeating decimals, such as 0.444 (repeating) equaling 4/9.
• 🔂 Converting more complex repeating decimals follows the same steps as simpler ones.
• 🔁 Multiplying the equation by a number with zeros can help align the decimals when converting more complex repeating decimals.

Transcript

good day welcome to Tech math Channel I'm Josh it's quite common in maths we ask our students to go through and change a decimal across to its equivalent fraction you know something like 0.5 is equal to2 or we have 0.25 is equal to a quarter but what do you do when you get something a bit more gnarly something looks like this say we had a decimal w... Read More

Questions & Answers

Q: How can we convert a repeating decimal to a fraction?

To convert a repeating decimal like 0.27 (repeating) to a fraction, we represent the repeating digits with a line over them, set up an equation, multiply by a certain number, subtract the equations, and simplify.

Q: Why do we multiply the equation by 100 when converting repeating decimals?

Multiplying by 100 allows us to align the decimals of the equation, making it easier to subtract one equation from the other and solve for the repeating pattern.

Q: Can we simplify the resulting fraction after converting a repeating decimal?

Yes, we can simplify the fraction by finding a common factor for both the numerator and denominator and dividing them by that factor.

Q: Are there patterns or tricks to converting repeating decimals to fractions?

Yes, there are patterns that emerge when converting repeating decimals to fractions. For example, 0.444 (repeating) is equal to 4/9, and 0.53 (repeating) is equal to 53/99.

Summary & Key Takeaways

• Converting decimals to fractions is a common math practice, but what happens when the decimal has repeating digits?

• To convert a repeating decimal to a fraction, we can represent the repeating digits with a line over them and set up an equation.

• By multiplying the equation by a certain number, subtracting one equation from the other, and simplifying, we can find the equivalent fraction.