2.66667 in fraction form

less than a minute read 21-02-2025

The decimal 2.66667 might seem tricky to convert into a fraction, but it's a straightforward process. This guide will walk you through the steps, explaining the logic behind each action. We'll tackle this seemingly complicated number and turn it into a simple fraction. Understanding this process will help you convert other repeating decimals as well.

Understanding Repeating Decimals

Before we begin, let's acknowledge that 2.66667 is an approximation. The number 2.666... (with the 6 repeating infinitely) is a recurring decimal. We'll address the slight difference at the end.

Step 1: Set up an Equation

Let's represent the decimal as 'x':

x = 2.66667

Since we're dealing with a repeating decimal (in the true form, at least), it would be best to instead consider the infinitely repeating version, x = 2.666...

Step 2: Multiply to Shift the Decimal

Multiply both sides of the equation by 10 to shift the repeating part of the decimal one place to the left:

10x = 26.666...

Step 3: Subtract to Eliminate the Repeating Part

Now, subtract the original equation (x = 2.666...) from the new equation (10x = 26.666...):

10x - x = 26.666... - 2.666...

This simplifies to:

9x = 24

Step 4: Solve for x

Divide both sides by 9 to solve for 'x':

x = 24/9

Step 5: Simplify the Fraction

Now, we simplify the fraction by finding the greatest common divisor (GCD) of 24 and 9, which is 3. Divide both the numerator and denominator by 3:

x = 8/3

Step 6: Addressing the Approximation

Remember, we started with 2.66667, an approximation of the repeating decimal 2.666... The fraction 8/3 represents the true repeating decimal 2.666... If you convert 8/3 to a decimal, you'll get 2.666666..., highlighting the slight difference.

Conclusion: 2.66667 as a Fraction

While 2.66667 isn't perfectly represented by a simple fraction due to the approximation, its closest fractional equivalent is 8/3. Understanding the steps involved in converting repeating decimals to fractions allows you to handle similar conversions with ease. Remember to always consider whether you are working with an approximation or a truly repeating decimal.