0.13 Repeating as a Fraction in Simplest Form
In mathematics, a repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. One such example is 0.13 repeating, which can be written as 0.1313... where the sequence "13" repeats indefinitely. But have you ever wondered how to express this repeating decimal as a fraction in its simplest form?
Converting 0.13 Repeating to a Fraction
To convert 0.13 repeating to a fraction, we can use a simple trick. Let's start by assuming that the repeating decimal is equal to a variable, say x:
x = 0.1313...
Next, we can multiply both sides of the equation by 100 to get:
100x = 13.1313...
Now, subtract the original equation from the new equation:
100x - x = 13.1313... - 0.1313...
This simplifies to:
99x = 13
Now, we can divide both sides by 99 to solve for x:
x = 13/99
Simplifying the Fraction
The fraction 13/99 is already in its simplest form. To see why, we can try to simplify it further by dividing both numerator and denominator by their greatest common divisor (GCD). The GCD of 13 and 99 is 1, so the fraction remains the same:
13 ÷ 1 = 13 99 ÷ 1 = 99
Therefore, the simplest form of 0.13 repeating as a fraction is:
13/99
In conclusion, we have successfully converted 0.13 repeating to a fraction in its simplest form, which is 13/99. This technique can be applied to convert any repeating decimal to a fraction, making it a powerful tool in mathematics.
