0.1 23 Repeating as a Fraction
Have you ever wondered how to convert a repeating decimal into a fraction? In this article, we'll explore how to do just that with the example of 0.1 23 repeating.
What is a Repeating Decimal?
A repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. In the case of 0.1 23 repeating, the sequence "23" repeats indefinitely. Repeating decimals can be converted into fractions, which can be useful in various mathematical applications.
Converting 0.1 23 Repeating to a Fraction
To convert 0.1 23 repeating to a fraction, we can use the following steps:
Step 1: Let x = 0.1 23 repeating
Let's start by letting x equal 0.1 23 repeating.
Step 2: Multiply x by 100
Next, we'll multiply x by 100 to get rid of the decimal point.
100x = 12.23 23 repeating
Step 3: Subtract x from 100x
Now, we'll subtract x from 100x to get:
99x = 12.12
Step 4: Simplify the fraction
Finally, we'll simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).
x = 12.12/99 x = 101/82
And that's it! We've successfully converted 0.1 23 repeating to a fraction, which is 101/82.
Conclusion
Converting repeating decimals to fractions can be a useful skill in mathematics. By following the steps outlined above, you can convert any repeating decimal into a fraction. Remember to always simplify your fraction by dividing both the numerator and the denominator by their GCD.
