0.16 6 Repeating as a Fraction
When dealing with repeating decimals, it's often useful to convert them into fractions. In this article, we'll explore how to convert 0.16 6, a repeating decimal, into a fraction.
What is a Repeating Decimal?
A repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. In the case of 0.16 6, the sequence "6" repeats indefinitely.
Converting 0.16 6 to a Fraction
To convert 0.16 6 to a fraction, we can use the following steps:
Step 1: Let x = 0.16 6
Let's assign the value 0.16 6 to a variable x.
Step 2: Multiply x by 100
Multiplying x by 100 gives us:
100x = 16.66...
Step 3: Subtract x from 100x
Subtracting x from 100x gives us:
99x = 16.5
Step 4: Divide by 99
Dividing both sides of the equation by 99 gives us:
x = 16.5/99
Step 5: Simplify the Fraction
Simplifying the fraction, we get:
x = 33/66
Final Answer
Therefore, 0.16 6 repeating as a fraction is equal to:
33/66
Simplified, this fraction can be written as:
1/2
There you have it! The repeating decimal 0.16 6 is equal to the fraction 1/2.
