0.39 Repeating as a Fraction
What is 0.39 Repeating?
0.39 repeating, also written as 0.39̄, is a decimal that has a repeating pattern of 39 indefinitely. This type of decimal is called a repeating decimal or a non-terminating decimal. In other words, 0.39 repeating has an infinite number of 39s after the decimal point.
Converting 0.39 Repeating to a Fraction
To convert 0.39 repeating to a fraction, we can use a simple algebraic method. Let's assume that the repeating decimal 0.39̄ is equal to a fraction x.
Step 1: Multiply by 100
Multiply both sides of the equation by 100 to get rid of the decimal point:
100x = 39.39̄
Step 2: Subtract the Original Equation
Subtract the original equation from the new equation:
100x - x = 39.39̄ - 0.39̄
This simplifies to:
99x = 39
Step 3: Divide by 99
Divide both sides of the equation by 99:
x = 39/99
Simplifying the Fraction
We can simplify the fraction 39/99 by dividing both the numerator and the denominator by their greatest common divisor, which is 3:
x = 13/33
Therefore, 0.39 repeating as a fraction is 13/33.
Conclusion
In conclusion, we have successfully converted the repeating decimal 0.39̄ to a fraction, which is 13/33. This conversion can be useful in various mathematical applications, such as algebra, geometry, and calculus.
