0.03 Recurring as a Fraction in Simplest Form
Recurring decimals, also known as repeating decimals, are decimal numbers that have a sequence of digits that repeats indefinitely. One such example is 0.03 recurring. In this article, we will explore how to convert 0.03 recurring as a fraction in its simplest form.
What is 0.03 Recurring?
0.03 recurring is a decimal number that can be written as 0.030303... (where the sequence of 03 repeats indefinitely). This type of decimal is known as a recurring decimal, because it repeats in a predictable pattern.
Converting 0.03 Recurring as a Fraction
To convert 0.03 recurring as a fraction, we can use the following steps:
Step 1: Let x = 0.030303... (1)
Let x be equal to the recurring decimal 0.030303...
Step 2: Multiply both sides by 100 (2)
Multiply both sides of the equation (1) by 100 to get:
100x = 3.030303...
Step 3: Subtract equation (1) from equation (2) (3)
Subtract equation (1) from equation (2) to get:
99x = 3
Step 4: Divide both sides by 99 (4)
Divide both sides of equation (3) by 99 to get:
x = 3/99
Step 5: Simplify the fraction (5)
Simplify the fraction 3/99 by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 3. This gives us:
x = 1/33
Therefore, 0.03 recurring can be written as a fraction in its simplest form as:
1/33
Conclusion
In this article, we have successfully converted 0.03 recurring as a fraction in its simplest form, which is 1/33. This is a useful technique for converting recurring decimals into fractions, and can be applied to other recurring decimals as well.
