0.123 Repeating as a Fraction: A Guide to Converting Repeating Decimals
Have you ever encountered a decimal that repeats indefinitely, such as 0.123 repeating, and wondered how to convert it to a fraction? In this article, we'll explore the steps to convert repeating decimals to fractions, using 0.123 repeating as an example.
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, where the sequence "123" repeats indefinitely.
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 x equal the repeating decimal 0.123 repeating.
Step 2: Multiply x by 1000
Multiply both sides of the equation by 1000, which is the power of 10 that is equal to the number of digits in the repeating sequence (in this case, 3 digits).
1000x = 123.123...
Step 3: Subtract x from 1000x
Subtract x from both sides of the equation to eliminate the repeating decimal.
999x = 123
Step 4: Solve for x
Divide both sides of the equation by 999 to solve for x.
x = 123/999
Step 5: Simplify the Fraction
Simplify the fraction by cancelling out any common factors.
x = 41/333
Therefore, 0.123 repeating is equal to the fraction 41/333.
Conclusion
Converting repeating decimals to fractions is a useful skill to have, and with these steps, you can easily convert any repeating decimal to a fraction. Remember to multiply by the power of 10 that is equal to the number of digits in the repeating sequence, and then solve for x to find the equivalent fraction.
Other Examples
- 0.23 repeating = 23/99
- 0.456 repeating = 456/999
- 0.789 repeating = 789/999
By following these steps, you can convert any repeating decimal to a fraction.
