0.171 Repeating as a Fraction
What is 0.171 Repeating?
0.171 repeating is a decimal number that has a pattern of digits that repeat indefinitely. Specifically, the digits "171" repeat over and over again. This type of decimal is known as a repeating decimal or a recurring decimal.
Converting 0.171 Repeating to a Fraction
To convert 0.171 repeating to a fraction, we can use a few different methods. One common method is to use the following formula:
x = 0.171171... (where x is the repeating decimal)
Multiply both sides of the equation by 1000 to get:
1000x = 171.171...
Subtract the original equation from the new equation to get:
999x = 171
Divide both sides by 999 to get:
x = 171/999
Simplifying the Fraction
We can simplify the fraction 171/999 by dividing both the numerator and the denominator by their greatest common divisor, which is 57.
171 ÷ 57 = 3
999 ÷ 57 = 17.5
So, the simplified fraction is:
3/17.5
We can simplify further by multiplying both the numerator and the denominator by 2 to get rid of the decimal in the denominator:
3 × 2 = 6
17.5 × 2 = 35
So, the final simplified fraction is:
6/35
Conclusion
In conclusion, the repeating decimal 0.171 repeating can be converted to the fraction 6/35. This fraction can be used in mathematical calculations and is a more concise way of representing the repeating decimal.
