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.