Math Problem Statement
3.8 3 repeating
Solution
The decimal (where 8 repeats indefinitely) can be expressed as a fraction. Let me show you how to convert it:
Step-by-step conversion of to a fraction:
- Let .
- Multiply both sides of the equation by 10 to shift the repeating decimal:
- Subtract the original equation from this new equation: This simplifies to:
- Solve for :
Thus, .
Would you like more details on this process or have any further questions?
Here are 5 related questions:
- How do you convert repeating decimals with different patterns (e.g., ) to fractions?
- What is the process for converting non-repeating decimals to fractions?
- Can all repeating decimals be expressed as fractions?
- How can you recognize if a decimal is terminating or repeating?
- How do you simplify fractions after converting from repeating decimals?
Tip: A repeating decimal is always a rational number, meaning it can be written as a fraction of two integers!
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Math Problem Analysis
Mathematical Concepts
Algebra
Repeating Decimals
Fractions
Formulas
x = 3.\overline{8}
10x = 38.\overline{8}
10x - x = 9x
x = \frac{35}{9}
Theorems
Rational Numbers Theorem (Repeating decimals can be expressed as fractions)
Suitable Grade Level
Grades 7-9