0.15 with 5 Repeating as a Fraction
Have you ever wondered how to convert a repeating decimal into a fraction? In this article, we will explore how to convert 0.15 with 5 repeating into a fraction.
What is a Repeating Decimal?
A repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. For example, 0.151515... is a repeating decimal because the sequence "15" repeats forever.
Converting 0.15 with 5 Repeating into a Fraction
To convert 0.15 with 5 repeating into a fraction, we can use the following steps:
Step 1: Identify the Repeating Sequence
The repeating sequence in this case is "15". Let's assign a variable to this sequence, say x.
Step 2: Set up the Equation
We can set up an equation using the variable x as follows:
100x = 15.1515...
Step 3: Isolate the Variable
To isolate the variable x, we can subtract 15.15 from both sides of the equation:
99x = 0.0015
Step 4: Divide by the Coefficient
Divide both sides of the equation by 99:
x = 0.0015/99
x = 1/660
Step 5: Simplify the Fraction
The fraction 1/660 can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 1 and 660 is 1, so the simplified fraction is:
x = 1/660
Therefore, 0.15 with 5 repeating as a fraction is equal to 1/660.
Conclusion
In this article, we have learned how to convert a repeating decimal into a fraction. We successfully converted 0.15 with 5 repeating into a fraction, which is equal to 1/660. This skill is important in mathematics and can be applied to various problems involving repeating decimals.
