Math Problem Statement

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

Solution

To convert 0.130.1\overline{3} (where only the 3 is recurring) into a fraction, let’s follow these steps:

  1. Let x=0.13x = 0.1\overline{3}.

    So, x=0.133333x = 0.133333\ldots

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

    10x=1.3333310x = 1.33333\ldots

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

    10xx=1.333330.1333310x - x = 1.33333\ldots - 0.13333\ldots

  4. This simplifies to:

    9x=1.29x = 1.2

  5. Now, solve for xx by dividing both sides by 9:

    x=1.29x = \frac{1.2}{9}

  6. Convert 1.21.2 to a fraction:

    x=12109=1290x = \frac{\frac{12}{10}}{9} = \frac{12}{90}

  7. Simplify 1290\frac{12}{90} by dividing the numerator and the denominator by their greatest common divisor, 6:

    x=215x = \frac{2}{15}

So, 0.13=2150.1\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.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Recurring Decimals
Fractions
Algebra

Formulas

x = 0.1\overline{3}
10x - x to eliminate recurring decimals
Simplifying fractions

Theorems

Conversion of recurring decimals to fractions

Suitable Grade Level

Grades 8-10