0.02222 Repeating as a Fraction
Introduction
Repeating decimals are a fascinating aspect of mathematics, and 0.02222 is one such decimal that has a unique property. In this article, we will explore how to convert 0.02222 repeating as a fraction.
What is a Repeating Decimal?
A repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. In the case of 0.02222, the sequence of digits "22" repeats indefinitely. This type of decimal is also known as a periodic decimal.
Converting 0.02222 to a Fraction
To convert 0.02222 to a fraction, we can use the following steps:
Step 1: Identify the repeating sequence
The repeating sequence in 0.02222 is "22".
Step 2: Write an equation
Let x = 0.02222. Then, multiply both sides of the equation by 100 to get rid of the decimal point.
100x = 2.2222
Step 3: Subtract the original equation from the new equation
Subtract x = 0.02222 from 100x = 2.2222 to get:
99x = 2.2
Step 4: Divide by the coefficient of x
Divide both sides of the equation by 99 to get:
x = 2.2/99
x = 2/9
Thus, 0.02222 repeating as a fraction is equal to 2/9.
Conclusion
In conclusion, we have successfully converted 0.02222 repeating as a fraction, which is equal to 2/9. This exercise demonstrates the importance of algebraic manipulations in converting repeating decimals to fractions.
