How to Convert Two-thirds (2/3) to a Percentage

In this comprehensive guide, we will explore the process of converting two-thirds (2/3) to a percentage. Understanding this conversion is essential for various mathematical and real-world applications. We will break down the steps and provide practical examples to ensure clarity.

Understanding Two-thirds (2/3) as a Fraction

The fraction two-thirds (2/3) represents the division of two by three. When expressed as a decimal, it is approximately 0.66666667, where the digit 6 repeats indefinitely.

Converting 2/3 to a Percentage

Converting a fraction to a percentage involves two main steps: converting the fraction to a decimal and then multiplying by 100. Here’s a breakdown of the process:

Step 1: Convert the Fraction to a Decimal

Dividing the numerator (2) by the denominator (3) gives us the decimal value:

2 ÷ 3 0.666666...

The result is a repeating decimal where the digit 6 keeps repeating.

Step 2: Convert the Decimal to a Percentage

To convert the decimal to a percentage, we multiply by 100:

0.666666... × 100 66.66666...%

Therefore, 2/3 is approximately 66.67% when rounded to two decimal places.

Practical Examples

Let's look at a few examples to reinforce our understanding:

Example 1: 2/3 as a Percentage

Divide the numerator by the denominator: 2 ÷ 3 0.666666... Multiply the result by 100: 0.666666... × 100 66.66666...%

Rounding to the nearest whole number, 2/3 as a percentage is approximately 67%.

Example 2: Detailed Steps for 2/3 to Percentage

Divide the numerator by the denominator: 2 ÷ 3 0.66666 Multiply by 100: 0.66666 × 100 66.667

Thus, 2/3 as a percentage is approximately 66.67%.

Example 3: Fraction to Percentage Conversion

Using the formula 23times;100200366223:

2/3 × 100 66 2/3, which rounds to 67.

Therefore, 2/3 as a percentage is approximately 67%.

Conclusion and Summary

In summary, to convert 2/3 to a percentage, we follow these steps:

Divide 2 by 3: 0.666666... Multiply the result by 100: 66.66666...%

Rounding this to the nearest whole number, 2/3 as a percentage is approximately 67%.

The final answer is: 2/3 67%.

FAQs

Q: Does 2/3 as a percentage round to 67 or 66.67?

A: Both 67 and 66.67 can be used, but 66.67 is more precise. The choice depends on the context and level of precision required.

Q: What is the repeating decimal of 2/3?

A: The repeating decimal of 2/3 is 0.666666..., where the digit 6 repeats indefinitely.

Q: How can I convert other fractions to percentages?

A: To convert any fraction to a percentage, divide the numerator by the denominator to get a decimal, then multiply by 100. For example, 3/4 would be 3 ÷ 4 0.75, then 0.75 × 100 75%.