Convert the Fraction 1/3 into a Percentage: Step-by-Step

Q: Why do I multiply by 100 instead of just converting to decimal?

A percentage means "per hundred" or out of 100. When you multiply by 100, you're finding how many parts out of 100 your fraction represents. The decimal 0.333 and percentage 33.33% are the same value, just expressed differently!

Q: Should I round 33.333... or keep it as 33.33%?

For most problems, 33.33% is the expected answer. The fraction 1/3 creates a repeating decimal (0.333...), so we typically round to two decimal places for percentages unless told otherwise.

Q: How can I check if 33.33% is really equal to 1/3?

Convert back! Take 33.33% and divide by 100: $ \frac{33.33}{100} = 0.3333 $. Then check: $ \frac{1}{3} = 0.3333... $ ✓

Q: What if I get confused about when to use fractions vs percentages?

Fractions show parts of a whole (like 1/3 of a pizza). Percentages show the same thing but out of 100 (like 33.33 out of 100 pieces). They're just different ways to express the same amount!

Q: Are there any shortcuts for common fractions?

Yes! Memorize these: 1/2 = 50%1/3 = 33.33%1/4 = 25%1/5 = 20% These come up frequently and will save you time!

Fraction to Percentage with Decimal Conversion

Given the fraction $\frac{1}{3}$ convert it into percentages

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert fractions to percentages

00:04 To convert a fraction to a percentage, multiply the fraction by 100

00:14 Proceed to calculate

00:22 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Given the fraction $\frac{1}{3}$ convert it into percentages

Step-by-step solution

To solve this problem, we'll convert the fraction $\frac{1}{3}$ into a percentage by following these steps:

Step 1: Identify the given fraction, which is $\frac{1}{3}$ .
Step 2: Use the formula for converting a fraction to a percentage: $\text{Percentage} = \left( \text{Fraction} \right) \times 100\%$ .
Step 3: Multiply the fraction by 100: $\frac{1}{3} \times 100 = \frac{100}{3}$ .
Step 4: Simplify $\frac{100}{3}$ . Divide 100 by 3 to obtain the decimal form, which is approximately 33.33.
Step 5: Express this result as a percentage: 33.33%.

Therefore, the fraction $\frac{1}{3}$ converted to a percentage is 33.33%.

When comparing this solution to the given multiple-choice options, the correct choice is:

33.33%

Final Answer

33.33%

Key Points to Remember

Essential concepts to master this topic

Formula: Multiply fraction by 100 to convert to percentage
Technique: Calculate $\frac{1}{3} \times 100 = \frac{100}{3} = 33.33$
Check: Verify 33.33% equals original fraction: 33.33/100 = 1/3 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to multiply by 100
Don't just convert 1/3 to decimal 0.333 and call it done = missing the % symbol! This gives you the decimal form, not the percentage. Always multiply by 100 and add the % symbol to complete the conversion.

Practice Quiz

Test your knowledge with interactive questions

Convert the fraction into a percentage:

$\frac{2}{100}=\text{?}$

FAQ

Everything you need to know about this question

Why do I multiply by 100 instead of just converting to decimal?

A percentage means "per hundred" or out of 100. When you multiply by 100, you're finding how many parts out of 100 your fraction represents. The decimal 0.333 and percentage 33.33% are the same value, just expressed differently!

Should I round 33.333... or keep it as 33.33%?

For most problems, 33.33% is the expected answer. The fraction 1/3 creates a repeating decimal (0.333...), so we typically round to two decimal places for percentages unless told otherwise.

How can I check if 33.33% is really equal to 1/3?

Convert back! Take 33.33% and divide by 100: $\frac{33.33}{100} = 0.3333$ . Then check: $\frac{1}{3} = 0.3333...$ ✓

What if I get confused about when to use fractions vs percentages?

Fractions show parts of a whole (like 1/3 of a pizza). Percentages show the same thing but out of 100 (like 33.33 out of 100 pieces). They're just different ways to express the same amount!

Are there any shortcuts for common fractions?

Yes! Memorize these:

1/2 = 50%
1/3 = 33.33%
1/4 = 25%
1/5 = 20%

These come up frequently and will save you time!

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