Compare negative three and five tenths repeating and negative ten thirds using symbols <, >, or =.

 negative three and five tenths repeating is less than negative ten thirds
 negative three and five tenths repeating is greater than negative ten thirds
 negative ten thirds is equal to negative three and five tenths repeating
 negative ten thirds is less than negative three and five tenths repeating

We are comparing two numbers: 
- **Negative three and five-tenths repeating**: This can be written as \(-3.\overline{5}\), which is a repeating decimal equivalent to \(-\frac{7}{2}\).
- **Negative ten thirds**: This is \(-\frac{10}{3}\).

To compare these two numbers, it's helpful to express them both as decimals or fractions.

1. **Negative three and five-tenths repeating**:
   \[
   -3.\overline{5} = -\frac{7}{2} \approx -3.5
   \]

2. **Negative ten thirds**:
   \[
   -\frac{10}{3} \approx -3.3333\ldots
   \]

Since \(-3.5\) is smaller than \(-3.3333\), we have:
\[
-3.\overline{5} < -\frac{10}{3}
\]

Therefore, the correct statement is:

**Negative three and five-tenths repeating is less than negative ten thirds**.

Would you like further clarification or details on this?

Here are five related questions for deeper understanding:

1. How do you convert repeating decimals into fractions?
2. Why are negative numbers larger when their absolute values are smaller?
3. How do you compare fractions with different denominators?
4. What is the difference between terminating and repeating decimals?
5. Can all repeating decimals be converted into fractions?

**Tip**: To compare two numbers more easily, convert them to either both fractions or both decimals.

Compare negative three and five tenths repeating and negative ten thirds using symbols <, >, or =.

This lesson explains how to compare negative repeating decimals and fractions, such as negative three and five-tenths repeating (-3.5̅) and negative ten thirds (-10/3). It covers key concepts in decimal and fraction conversion and the properties of negative numbers. Suitable for students in 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