0.1666 Recurring as a Fraction
The decimal 0.1666 recurring, also known as a repeating decimal, is a number that has a sequence of digits that repeats indefinitely. In this case, the sequence "6" repeats indefinitely. But what is the equivalent fraction of this repeating decimal?
Converting 0.1666 Recurring to a Fraction
To convert 0.1666 recurring to a fraction, we can use the following steps:
Let x = 0.1666...
Since the sequence "6" repeats indefinitely, we can set up an equation by multiplying both sides by 10:
10x = 1.666...
Now, subtract x from both sides to get:
9x = 1.5
Divide both sides by 9 to solve for x:
x = 1.5 ÷ 9 x = 1/6
So, the equivalent fraction of 0.1666 recurring is 1/6.
Properties of the Fraction 1/6
The fraction 1/6 is a proper fraction, where the numerator (1) is less than the denominator (6). It is also a unit fraction, where the numerator is 1.
The decimal equivalent of 1/6 is 0.1666 recurring, which means that the fraction can be converted back to the original repeating decimal.
Real-World Applications of 1/6
The fraction 1/6 has many real-world applications, such as:
- Measurement: 1/6 of a foot is equal to 2 inches.
- Cooking: A recipe may require 1/6 of a teaspoon of a certain ingredient.
- Music: 1/6 of a beat is a common rhythmic pattern in music.
- Finance: 1/6 of a year is equivalent to 2 months, which is a common payment period for bills or loans.
In conclusion, the repeating decimal 0.1666 recurring is equivalent to the fraction 1/6, which has many practical applications in various fields.
