0.08 Repeating as a Fraction in Simplest Form
In mathematics, repeating decimals can be converted into fractions. One such example is 0.08 repeating, which can be written as a fraction in its simplest form.
** Understanding Repeating Decimals **
A repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. For example, 0.08 repeating can be written as 0.080808081... where the sequence "08" repeats indefinitely.
Converting 0.08 Repeating to a Fraction
To convert 0.08 repeating to a fraction, we can use the following steps:
Step 1: Let x = 0.0808...
Let x = 0.0808... be the repeating decimal.
Step 2: Multiply x by 100
Multiply both sides of the equation by 100 to get:
100x = 8.0808...
Step 3: Subtract x from 100x
Subtract x from 100x to get:
99x = 8
Step 4: Divide by 99
Divide both sides of the equation by 99 to get:
x = 8/99
Step 5: Simplify the Fraction
The fraction 8/99 is already in its simplest form.
Result
Therefore, 0.08 repeating as a fraction in its simplest form is:
8/99
This fraction can be used in various mathematical operations, such as addition, subtraction, multiplication, and division.
Conclusion
In conclusion, converting 0.08 repeating to a fraction is a simple process that involves multiplying, subtracting, and dividing. The resulting fraction, 8/99, is in its simplest form and can be used in various mathematical applications.
