0.171 Recurring as a Fraction
The decimal number 0.171 recurring, also denoted as 0.171..., is a repeating decimal that has a finite fractional equivalent. In this article, we will explore how to convert 0.171 recurring to a fraction.
What is a Recurring Decimal?
A recurring decimal, also known as a repeating decimal, is a decimal number that has a sequence of digits that repeats indefinitely. For example, 0.171..., 0.234234..., and 0.567567... are all examples of recurring decimals.
Converting 0.171 Recurring to a Fraction
To convert 0.171 recurring to a fraction, we can use the following steps:
Step 1: Let x = 0.171...
Let x = 0.171... be the recurring decimal.
Step 2: Multiply x by 1000
Multiply both sides of the equation by 1000 to get:
1000x = 171.171...
Step 3: Subtract x from 1000x
Subtract x from both sides of the equation to get:
999x = 171
Step 4: Divide by 999
Divide both sides of the equation by 999 to get:
x = 171/999
Simplify the Fraction
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor (GCD), which is 3. Therefore, we get:
x = 57/333
Final Answer
Therefore, 0.171 recurring is equal to the fraction 57/333.
