Math Problem Statement
Write 0. 32 overbar as a fraction in simplest form.
Solution
To express (the repeating decimal ) as a fraction, we can follow these steps:
Step 1: Let
We define as the repeating decimal:
Step 2: Eliminate the repeating decimal
Since the repeating part is 2 digits long ("32"), we multiply both sides of the equation by 100 (because the repeat length is 2 digits):
Step 3: Subtract the original equation from the new equation
Now subtract from :
Step 4: Solve for
Now, solve for by dividing both sides of the equation by 99:
Final Answer:
The fraction equivalent of is:
This fraction is already in its simplest form because 32 and 99 have no common factors other than 1.
Would you like to see more examples, or need further clarification? Here are some related questions:
- How can we convert into a fraction?
- What is the fractional representation of ?
- How would you convert into a fraction?
- What is the general method for converting repeating decimals to fractions?
- What do we mean when a decimal is called "repeating"?
Tip: If the decimal repeats for digits, multiply by to eliminate the repeating part before subtracting.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Repeating Decimals
Fractions
Algebra
Formulas
x = 0.323232...
100x = 32.323232...
x = 32/99
Theorems
Converting repeating decimals to fractions
Suitable Grade Level
Grades 7-9