How to Convert Repeating Decimals to Fractions

TL;DR

Convert repeating decimals into fractions by multiplying the decimal by powers of ten to shift it left and then subtracting the original. This process eliminates the repeating digits, allowing you to simplify the resulting equation to find the fraction equivalent.

Transcript

Hello. I'm Professor Von Schmohawk and welcome to Why U. We have seen that multiplying any decimal number by ten shifts each digit in the number one column to the left. In the last lecture, we used this trick to convert decimal numbers with a finite number of digits into fractions. In this lecture, we will see how to convert "repeating" decimal num... Read More

Key Insights

• 🔁 Repeating decimals can be converted into fractions using multiplication and subtraction.
• 😥 Multiplying by powers of ten helps eliminate the repeating digits after the decimal point.
• 🔁 The resulting equation helps find the fraction equivalent of the repeating decimal number.
• 😘 Fractions obtained can be further simplified to their lowest terms.
• 🦻 Understanding this conversion process aids in mathematical operations and calculations.
• 💁 The most common repeating decimal, 0.333..., equals 1/3 in fractional form.
• 🔁 Complex repeating decimals can be reduced to simpler fractions using factoring techniques.

Questions & Answers

Q: How are repeating decimal numbers converted into fractions?

Repeating decimals are converted by shifting numbers to the left through multiplication and subtraction. This process eliminates the repeating digits and allows representation as fractions.

Q: Why is multiplication by ten a key step in converting repeating decimals?

Multiplying the decimal number by ten shifts the digits to the left, which helps eliminate the repeating digits after the decimal point, making it easier to convert to a fraction.

Q: How can fractions be simplified after converting repeating decimals?

Fractions obtained from repeating decimals can be simplified by reducing them to their simplest form using common factors between the numerator and denominator.

Q: Why is it important to understand the process of converting repeating decimals to fractions?

Understanding this process helps in converting decimal representations into more easily comprehensible and manipulable fraction forms, aiding in mathematical calculations.

Summary & Key Takeaways

• Decimal numbers with repeating digits are converted to fractions by multiplying and subtracting.

• Multiplying by ten and subtracting eliminates repeating digits after the decimal point.

• The resulting equation helps determine the fraction equivalent of the repeating decimal number.