0.1 7 Repeating as a Fraction
Introduction
The decimal number 0.1 7 repeating is a non-terminating, recurring decimal that can be expressed as a fraction. In this article, we will explore how to convert 0.1 7 repeating into a fraction.
What is a Repeating Decimal?
A repeating decimal is a decimal number that has a sequence of digits that repeats indefinitely. In the case of 0.1 7 repeating, the sequence "17" repeats forever.
Converting Repeating Decimals to Fractions
To convert a repeating decimal to a fraction, we can use the following steps:
- Let x = the repeating decimal (in this case, 0.1 7)
- Multiply both sides of the equation by 10^k, where k is the number of repeating digits (in this case, 2)
- Subtract the original equation from the new equation
- Simplify the resulting fraction
Converting 0.1 7 Repeating to a Fraction
Let's follow the steps above to convert 0.1 7 repeating to a fraction:
Step 1: Let x = 0.1 7
x = 0.1 7
Step 2: Multiply by 10^2
100x = 17.17
Step 3: Subtract the original equation
100x - x = 17.17 - 0.1 7
Step 4: Simplify the fraction
99x = 17 x = 17/99
Therefore, 0.1 7 repeating is equal to 17/99.
Conclusion
In conclusion, we have successfully converted the repeating decimal 0.1 7 into a fraction, which is 17/99. This demonstrates the relationship between repeating decimals and fractions, and provides a useful technique for converting between the two forms.
