0.123 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 convert 0.123 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, 0.123123123... is a repeating decimal because the sequence "123" repeats over and over again.
Converting 0.123 Repeating into a Fraction
To convert 0.123 repeating into a fraction, we can use the following steps:
Step 1: Let x = 0.123 repeated
Let's start by letting x equal 0.123 repeated.
Step 2: Multiply x by 1000
Next, let's multiply x by 1000 to get:
1000x = 123.123 repeated
Step 3: Subtract x from 1000x
Now, let's subtract x from 1000x to get:
999x = 123
Step 4: Divide both sides by 999
Finally, let's divide both sides of the equation by 999 to get:
x = 123/999
Step 5: Simplify the fraction
We can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 3:
x = 41/333
Therefore, 0.123 repeating as a fraction is 41/333.
Conclusion
Converting repeating decimals into fractions is an important skill in mathematics. By following these simple steps, you can convert any repeating decimal into a fraction. Remember to multiply by a power of 10, subtract, and simplify to get your final answer!
