Convert 1.333333333 To A Fraction Easily
Table of Contents :
Converting decimals to fractions can seem intimidating, but it is a straightforward process once you understand the steps involved. In this article, we will explore how to convert the repeating decimal 1.333333333 to a fraction in a simple and easy-to-follow way. Let’s dive in! ✨
Understanding Repeating Decimals
A repeating decimal is a decimal fraction that eventually repeats a sequence of digits. The decimal 1.333333333 is an example of a repeating decimal, where the digit "3" continues indefinitely. We denote this repeating decimal in a more compact form as 1.3̅, where the line over the "3" indicates that it repeats.
Steps to Convert a Repeating Decimal to a Fraction
The following steps will help you convert 1.3̅ into a fraction.
Step 1: Set Up an Equation
First, let’s set up an equation. We will assign the repeating decimal to a variable:
Let ( x = 1.3̅ )
Step 2: Eliminate the Repeating Part
To eliminate the repeating part, we can multiply both sides of the equation by a power of 10 that shifts the decimal point to the right. Since the "3" repeats every single digit, we can multiply by 10:
[ 10x = 13.3̅ ]
Step 3: Subtract the Two Equations
Now we have two equations:
- ( x = 1.3̅ )
- ( 10x = 13.3̅ )
Next, we will subtract the first equation from the second:
[ 10x - x = 13.3̅ - 1.3̅ ]
This simplifies to:
[ 9x = 12 ]
Step 4: Solve for ( x )
Now we can isolate ( x ):
[ x = \frac{12}{9} ]
Step 5: Simplify the Fraction
The fraction ( \frac{12}{9} ) can be simplified by finding the greatest common divisor (GCD) of the numerator and denominator, which is 3:
[ x = \frac{12 \div 3}{9 \div 3} = \frac{4}{3} ]
Conclusion: The Result
Thus, we have successfully converted the repeating decimal 1.3̅ into the fraction (\frac{4}{3})! 🎉
To summarize, here’s a quick breakdown of the process:
| Step | Action | Equation |
|---|---|---|
| 1 | Set up the equation | ( x = 1.3̅ ) |
| 2 | Multiply to eliminate repeating part | ( 10x = 13.3̅ ) |
| 3 | Subtract the equations | ( 9x = 12 ) |
| 4 | Solve for ( x ) | ( x = \frac{12}{9} ) |
| 5 | Simplify the fraction | ( x = \frac{4}{3} ) |
Important Note
Converting decimals to fractions is a useful skill, especially in mathematics, engineering, and various applications where exact values are necessary instead of approximate decimal representations.
By practicing these steps, you will find it easier to convert not just 1.3̅ but other repeating and non-repeating decimals into fractions. Remember, the key is to set up your equations carefully and simplify your results accurately.
Now that you know how to convert repeating decimals to fractions, try your hand at some other examples! 😊