Converting 0.01 Repeating Decimal to a Fraction in Simplest Form
In mathematics, repeating decimals can be converted to fractions in simplest form. This article will guide you through the process of converting 0.01 repeating decimal to a fraction in simplest form.
What is a Repeating Decimal?
A repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. In the case of 0.01, the sequence of digits "01" repeats indefinitely, making it a repeating decimal.
Converting 0.01 Repeating Decimal to a Fraction
To convert 0.01 repeating decimal to a fraction, we can use the following steps:
Step 1: Let x = 0.01
Let's assign the repeating decimal 0.01 to a variable x.
Step 2: Multiply x by 100
Multiply both sides of the equation by 100 to get:
100x = 1.01
Step 3: Subtract x from both sides
Subtract x from both sides of the equation to get:
99x = 1
Step 4: Divide both sides by 99
Divide both sides of the equation by 99 to get:
x = 1/99
Simplify the Fraction
The fraction 1/99 is already in simplest form. Therefore, the 0.01 repeating decimal is equal to the fraction 1/99.
Conclusion
In conclusion, we have successfully converted the 0.01 repeating decimal to a fraction in simplest form, which is 1/99. This process can be applied to any repeating decimal to convert it to a fraction in simplest form.
