The decimal number 0.16666 is a repeating decimal, where the digit 6 repeats infinitely. This type of decimal can be expressed as a fraction in its simplest form. Understanding how to convert such decimals into fractions is a fundamental concept in mathematics, offering a way to represent and manipulate numbers in various contexts.
To convert 0.16666 into a fraction, we can follow a systematic approach. First, we recognize that the repeating pattern is the digit 6. We then set up an equation where 'x' represents the repeating decimal:
Let x = 0.16666...
Multiplying both sides by 10 gives:
10x = 1.6666...Subtracting the original equation from this new equation eliminates the repeating part:
10x - x = 1.6666... - 0.16666...This simplifies to:
9x = 1.5Now, we can solve for 'x' by dividing both sides by 9:
x = 1.5 / 9Simplifying the fraction 1.5/9 by dividing both the numerator and denominator by their greatest common divisor, which is 3, we get:
x = 0.5 / 3Therefore, the decimal 0.16666 can be expressed as the fraction 0.16666 as a fraction 5/3.
This conversion demonstrates a useful technique for handling repeating decimals, which can be applied to various mathematical and real-world problems, especially in fields where precise numerical representations are essential.