0.123 Repeating as a Fraction
The decimal number 0.123 repeating, also represented as 0.123..., is a non-terminating repeating decimal. In this article, we will explore how to convert 0.123 repeating as a fraction.
What is a Repeating Decimal?
A repeating decimal, also known as a recurring decimal, is a decimal number that has a sequence of digits that repeats indefinitely. For example, 0.123..., 0.456..., or 0.789... are all repeating decimals.
Converting 0.123 Repeating as a Fraction
To convert 0.123 repeating as a fraction, we can use the following method:
Let x = 0.123...
Since the sequence of digits repeats, we can multiply x by 1000 to get:
1000x = 123.123...
Now, subtract x from 1000x to eliminate the decimal part:
1000x - x = 123.123... - 0.123...
This simplifies to:
999x = 123
Divide both sides by 999:
x = 123/999
Simplify the fraction:
x = 41/333
Therefore, 0.123 repeating as a fraction is 41/333.
Properties of the Fraction
The fraction 41/333 has some interesting properties:
- It is an infinite fraction, meaning it cannot be simplified further.
- It is a rational number, which means it can be expressed as the ratio of two integer numbers (41 and 333).
- It is a non-terminating fraction, meaning it has an infinite number of decimal places.
In conclusion, 0.123 repeating as a fraction is equal to 41/333, which has some fascinating properties as a rational and infinite fraction.
