Converting 0.08 Repeating Decimal to Fraction
In mathematics, converting a repeating decimal to a fraction is a fundamental concept in number theory. A repeating decimal is a decimal representation of a number that has a sequence of digits that repeats indefinitely. In this article, we will learn how to convert 0.08 repeating decimal to a fraction.
Understanding Repeating Decimals
A repeating decimal can be represented by a dot above the repeating digit(s) or by using an ellipsis (...). For example, the decimal representation of 0.08 repeating can be written as:
0.080808...
or
0.08̇
Converting 0.08 Repeating Decimal to Fraction
To convert 0.08 repeating decimal to a fraction, we can use the following steps:
Step 1: Let x = 0.080808...
Let x be the given repeating decimal.
Step 2: Multiply x by 100
Multiply both sides of the equation by 100 to get rid of the decimal point:
100x = 8.080808...
Step 3: Subtract x from 100x
Subtract x from both sides of the equation to eliminate the repeating part:
99x = 8
Step 4: Divide by 99
Divide both sides of the equation by 99:
x = 8/99
Therefore, the fraction equivalent of 0.08 repeating decimal is 8/99.
Conclusion
In this article, we have successfully converted 0.08 repeating decimal to a fraction, which is 8/99. This process can be applied to any repeating decimal to convert it to a fraction. It is essential to understand this concept in mathematics, as it has various applications in algebra, arithmetic, and other branches of mathematics.
