.01 Repeating as a Fraction in Simplest Form
In mathematics, repeating decimals can be converted into fractions. In this article, we will explore how to convert .01 repeating into a fraction in its simplest form.
What is .01 Repeating?
.01 repeating, also written as .010101…, is a decimal that has an infinite number of 01 sequences. This pattern of 01 repeating infinitely is denoted by a horizontal line above the decimal point.
Converting .01 Repeating to a Fraction
To convert .01 repeating into a fraction, we can use the following steps:
Step 1: Let x = .01 Repeating
Let x = .01 repeating = .010101…
Step 2: Multiply x by 100
Multiply both sides of the equation by 100 to get:
100x = 1.010101…
Step 3: Subtract x from Both Sides
Subtract x from both sides of the equation to get:
99x = 1
Step 4: Divide 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 its simplest form.
Answer
.01 repeating as a fraction in simplest form is 1/99.
In conclusion, .01 repeating can be converted into a fraction in its simplest form, which is 1/99. This process involves multiplying and subtracting the decimal to eliminate the repeating pattern, and then simplifying the resulting fraction.
