0.123 Repeating as a Fraction in Simplest Form
Have you ever wondered how to convert a repeating decimal into a fraction in its simplest form? Well, you're in luck because we're about to explore how to do just that with the example of 0.123 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 0.123 repeating, the sequence "123" repeats forever. This type of decimal is also known as a recurring decimal.
Converting 0.123 Repeating to a Fraction
To convert 0.123 repeating to a fraction, we can use the following steps:
Step 1: Let x = 0.123 Repeating
Let's start by letting x equal our repeating decimal.
Step 2: Multiply x by 1000
Next, we'll multiply x by 1000 to get rid of the decimal point.
1000x = 123.123
Step 3: Subtract x from 1000x
Now, we'll subtract x from 1000x to get:
999x = 123
Step 4: Solve for x
Finally, we'll solve for x by dividing both sides of the equation by 999.
x = 123/999
Step 5: Simplify the Fraction
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 123 and 999 is 3.
x = (123 ÷ 3)/(999 ÷ 3) x = 41/333
And that's it! We've successfully converted 0.123 repeating to a fraction in its simplest form: 41/333.
Conclusion
Converting a repeating decimal to a fraction in its simplest form may seem daunting, but with the right steps, it can be a breeze. By following the steps outlined above, you can convert any repeating decimal into a fraction. Remember to always simplify your fraction by dividing by the greatest common divisor to get the simplest form.
