An engineer measured the length of piece of wire as 0.36 recurring decimal. Convert the length into a fraction

The recurring decimal \( 0.36\overline{6} \) can be converted into a fraction as follows:

Let \( x = 0.36\overline{6} \). 

### Step 1: Multiply to move the decimal point
To eliminate the recurring part, consider \( 100x \):
\[
100x = 36.66\overline{6}
\]

### Step 2: Subtract to get rid of the repeating part
\[
100x - x = 36.66\overline{6} - 0.36\overline{6}
\]
\[
99x = 36.3
\]

### Step 3: Solve for \( x \)
\[
x = \frac{36.3}{99}
\]

Since \( 36.3 \) can be written as \( \frac{363}{10} \), we get:
\[
x = \frac{363}{990}
\]

### Step 4: Simplify the fraction
Divide the numerator and the denominator by their greatest common divisor, which is 9:
\[
x = \frac{363 \div 9}{990 \div 9} = \frac{121}{330}
\]

This fraction can be further simplified by dividing by 11:
\[
x = \frac{11}{30}
\]

So, the length of the wire as a fraction is:
\[
\boxed{\frac{11}{30}}
\]

Would you like further details or explanations?

Here are some related questions:
1. How do you convert a recurring decimal like \( 0.333\overline{3} \) into a fraction?
2. What is the general process for converting a decimal with more than one repeating digit into a fraction?
3. How can we verify that \( \frac{11}{30} \) is equivalent to \( 0.36\overline{6} \)?
4. Why do recurring decimals convert to rational numbers (fractions)?
5. How do you simplify fractions to their lowest terms?

**Tip:** When converting a recurring decimal to a fraction, remember to write down the repeating part as \( x \) and then manipulate it by multiplying by powers of 10.

An engineer measured the length of piece of wire as 0.36 recurring decimal. Convert the length into a fraction.

Learn how to convert the recurring decimal 0.36 (with repeating 6) into a simplified fraction. This detailed step-by-step solution covers key concepts such as fraction conversion, recurring decimals, and fraction simplification. Suitable for students in Grades 6-8.

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