.20 Repeating Decimal as a Fraction
A repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. In this article, we will explore how to convert the repeating decimal .20 to a fraction.
What is a Repeating Decimal?
A repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. For example, the decimal .12341234... is a repeating decimal because the sequence "1234" repeats indefinitely.
Converting a Repeating Decimal to a Fraction
To convert a repeating decimal to a fraction, we can use the following steps:
Step 1: Let the repeating decimal be x
Let the repeating decimal .20 be x.
Step 2: Multiply both sides by 10
Multiply both sides of the equation by 10 to get:
10x = 2.00
Step 3: Subtract x from both sides
Subtract x from both sides of the equation to get:
10x - x = 2.00 - .20
Step 4: Simplify the equation
Simplify the equation to get:
9x = 1.80
Step 5: Divide both sides by 9
Divide both sides of the equation by 9 to get:
x = 1.80/9
x = 0.20
Step 6: Write the fraction
Write the fraction by dividing the numerator by the denominator:
x = 2/10
x = 1/5
Therefore, the repeating decimal .20 is equal to the fraction 1/5.
Conclusion
In conclusion, we have successfully converted the repeating decimal .20 to the fraction 1/5. This method can be used to convert any repeating decimal to a fraction.
