0.1388 Repeating as a Fraction
The repeating decimal 0.1388 can be converted into a fraction. But before we dive into that, let's understand what repeating decimals are.
What are Repeating Decimals?
Repeating decimals are decimal numbers that have a sequence of digits that repeat infinitely. For example, 0.1388 is a repeating decimal because the sequence "1388" repeats indefinitely. Repeating decimals can be converted into fractions, and in this article, we'll show you how to do that for 0.1388.
Converting 0.1388 into a Fraction
To convert 0.1388 into a fraction, we can use the following steps:
Step 1: Let x = 0.1388
Let's assume that x = 0.1388. This will help us to create an equation that we can use to convert the decimal into a fraction.
Step 2: Multiply x by 10000
Multiply both sides of the equation by 10000, which is the place value of the repeating sequence "1388". This will give us:
10000x = 1388.1388
Step 3: Subtract x from both sides
Subtract x from both sides of the equation to get:
9999x = 1388
Step 4: Divide both sides by 9999
Now, divide both sides of the equation by 9999 to get:
x = 1388/9999
Step 5: Simplify the fraction
Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 1111. This gives us:
x = 1388/9999 = 4/36 = 1/9
Therefore, the repeating decimal 0.1388 is equal to the fraction 1/9.
Conclusion
In this article, we've shown you how to convert the repeating decimal 0.1388 into a fraction. By following the steps outlined above, you can convert any repeating decimal into a fraction. Repeating decimals are a fundamental concept in mathematics, and understanding how to convert them into fractions is an important skill to have in your mathematical toolkit.
