Decimal to Fraction Conversion: Reflecting on Representing Repeating Decimals
How can we represent a repeating decimal as a fraction?
Given the repeating decimal 0.333333..., can you express it as a fraction?
Answer:
The repeating decimal 0.333333... can be represented as the fraction 1/3.
When dealing with repeating decimals, it's important to understand how to convert them into fractions. In this case, the repeating decimal 0.333333... can be converted to the fraction 1/3. This conversion is based on the concept of ratios and division.
As we know, the decimal 0.333333... has the digit 3 repeating infinitely. To represent this as a fraction, we can set it up as follows:
x = 0.333333...
10x = 3.333333...
Subtracting the first equation from the second equation:
10x - x = 3.333333... - 0.333333...
9x = 3
x = 3/9
x = 1/3
Therefore, the repeating decimal 0.333333... is equivalent to the fraction 1/3. This shows that fractions and decimals are different ways to express the same mathematical value. Understanding how to convert between them is essential in mathematics and various real-life applications.