0.157 Repeating as a Fraction
Definition of a Repeating Decimal
A repeating decimal is a decimal number that has a sequence of digits that repeats indefinitely. For example, 0.157 is a repeating decimal because the sequence "157" repeats indefinitely.
Converting a Repeating Decimal to a Fraction
To convert a repeating decimal to a fraction, we can use the following steps:
- Let the repeating decimal be x.
- Multiply both sides of the equation by 10^k, where k is the number of digits in the repeating sequence.
- Subtract the original equation from the new equation.
- Simplify the resulting equation to get the fraction.
Converting 0.157 Repeating to a Fraction
Let's convert 0.157 repeating to a fraction using the steps above.
Step 1: Let x = 0.157 repeating
x = 0.157157...
Step 2: Multiply both sides by 10^3
1000x = 157.157157...
Step 3: Subtract the original equation from the new equation
999x = 157
Step 4: Simplify the resulting equation
x = 157/999
Therefore, 0.157 repeating is equal to the fraction 157/999.
Conclusion
In this article, we have learned how to convert a repeating decimal to a fraction. We have applied this concept to convert 0.157 repeating to a fraction, which is equal to 157/999. This concept is essential in mathematics, particularly in algebra and number theory.
