The decimal \( 6.1667 \) can be expressed as a fraction. Since \( 6.1667 \) is a repeating decimal, the exact value is \( 6\frac{1}{6} \).

Here's how to express it as a fraction:

1. Let \( x = 6.1667 \).
2. Multiply both sides by 10,000 to move the decimal four places to the right:

   \[
   10,000x = 61667
   \]

3. Now subtract \( x = 6.1667 \) from \( 10,000x = 61667 \):

   \[
   10,000x - x = 61667 - 6.1667
   \]

   \[
   9999x = 61660.8333
   \]

4. Simplify the equation:

   \[
   x = \frac{61660.8333}{9999}
   \]

5. Simplify further to get the fraction \( x = \frac{37}{6} \).

Thus, \( 6.1667 \) as a fraction is \( 6\frac{1}{6} \), which equals \( \frac{37}{6} \).

Would you like more details or have any questions? Here are some related questions:

1. How do you convert a repeating decimal to a fraction?
2. What is the difference between terminating and repeating decimals?
3. How do you simplify fractions?
4. What are mixed numbers, and how are they converted to improper fractions?
5. How can you add and subtract mixed numbers?

**Tip:** To convert a repeating decimal to a fraction, express the repeating part as a geometric series and then simplify.

Learn how to convert the repeating decimal 6.1667 to a fraction step-by-step. Understand the concept of repeating decimals and fraction conversion in mathematics. Suitable for Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation