What is 1/3 as a percentage?

Hello, young mathematicians! Let's dive into the captivating world of fractions and percentages. Get ready through the methods for converting 1/3 into a percentage with us!

Answer: 1/3 as a percentage is 33.333…%

When you have a fraction like 1/3, it means you have 1 parts out of a total of 3 parts. To express this fraction as a percentage, you're comparing it to a whole of 100 parts. So, you're calculating how many out of those 100 parts your fraction represents.

In the case of 1/3, when you convert it to an equivalent fraction with a denominator of 100, you get 33.333…%.

There are many methods you can apply, and they allow you to convert fractions to percentages, helping you relate fractions to the concept of parts out of 100.

Method 1: Using Equivalent Fractions

Step 1: 

Write down the fraction: 1/3

Step 2: 

Create an equivalent fraction with a denominator of 100. To do this, determine what number you need to multiply the 3 by to reach 100. In this case, you'd need to multiply both the numerator and denominator by 333.3333333333333.

Step 3:

The numerator of the equivalent fraction represents the part out of 100, so the percentage is 33.333…%.

So, 1/3 as a percentage is 33.333…%.

Method 2: Divide and Multiply by 100

Step 1: 

Write down the fraction: 1/3

Step 2: 

Divide the numerator by the denominator: 1 ÷ 3 = 33.333…%

Step 3: 

Multiply the result by 100 to express it as a percentage: 33.333…% * 100 = 33.333…%

Again, you get the same result: 1/3 as a percentage is 33.333…%.

Method 3: Fraction to Decimal to Percentage

Step 1: 

Write down the fraction: 1/3

Step 2: 

Convert the fraction to a decimal using division: 1 ÷ 3 = 33.333…%

Step 3: 

Convert the decimal to a percentage by multiplying it by 100: 33.333…% * 100 = 33.333…%

Each method confirms that 1/3 as a percentage is 33.333…%.

Remember, practice makes perfect! The more you work with these conversions, the more comfortable you'll become with the process.

Common Core State Standards

Grade 7

Ratios and Proportional Relationships (7.RP)