0.034 Recurring as a Fraction in Simplest Form
When dealing with recurring decimals, it's often helpful to convert them to fractions in their simplest form. In this article, we'll explore how to convert 0.034 recurring to a fraction in its simplest form.
What is a recurring decimal?
A recurring decimal is a decimal that has a sequence of digits that repeats indefinitely. In the case of 0.034 recurring, the sequence "34" repeats indefinitely: 0.0343434... .
Converting 0.034 recurring to a fraction
To convert 0.034 recurring to a fraction, we can use the following steps:
Step 1: Let x = 0.034 recurring
Let x = 0.0343434... .
Step 2: Multiply x by 100
Multiply x by 100 to get:
100x = 3.4343434... .
Step 3: Subtract x from 100x
Subtract x from 100x to get:
99x = 3.4
Step 4: Divide by 99
Divide both sides by 99 to get:
x = 3.4/99
Step 5: Simplify the fraction
Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 1:
x = 3/25
So, 0.034 recurring can be expressed as a fraction in its simplest form as 3/25.
Conclusion
In conclusion, we have successfully converted 0.034 recurring to a fraction in its simplest form, which is 3/25. This conversion can be useful in a variety of mathematical operations and applications.
