Convert 0,13 to common fraction,when only 3 is recurring 

To convert \( 0.1\overline{3} \) (where only the 3 is recurring) into a fraction, let’s follow these steps:

1. Let \( x = 0.1\overline{3} \).

   So, \( x = 0.133333\ldots \)

2. Multiply both sides by 10 to shift the decimal point one place:

   \[ 10x = 1.33333\ldots \]

3. Subtract the original equation from this new equation to eliminate the recurring decimal:

   \[ 10x - x = 1.33333\ldots - 0.13333\ldots \]

4. This simplifies to:

   \[ 9x = 1.2 \]

5. Now, solve for \( x \) by dividing both sides by 9:

   \[ x = \frac{1.2}{9} \]

6. Convert \( 1.2 \) to a fraction:

   \[ x = \frac{\frac{12}{10}}{9} = \frac{12}{90} \]

7. Simplify \( \frac{12}{90} \) by dividing the numerator and the denominator by their greatest common divisor, 6:

   \[ x = \frac{2}{15} \]

So, \( 0.1\overline{3} = \frac{2}{15} \).

Would you like more details or have any questions?

---

Here are some related questions:

1. How can you convert other recurring decimals to fractions?
2. What is the general formula for converting single-digit recurring decimals?
3. How would the approach differ for a decimal where multiple digits recur?
4. How do you simplify fractions effectively?
5. Can recurring decimals always be represented as fractions?

**Tip:** When converting recurring decimals to fractions, multiply by powers of 10 that align the recurring digits for easy subtraction.

Convert 0.13 to a common fraction, when only 3 is recurring.

Learn how to convert the recurring decimal 0.1\overline{3} to a fraction in a step-by-step process. This guide covers methods for eliminating recurring decimals, simplifying fractions, and using algebraic approaches. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation