Convert 3.1% to a Fraction: Finding the Equivalent /100 Form

Q: Why can't I just remove the decimal and write 31/100?

Because 3.1 and 31 are different numbers! When you write $ \frac{31}{100} $, you're saying 31%, which is 10 times bigger than 3.1%. Always keep decimals exactly as they appear.

Q: Is it okay to have a decimal in the numerator of a fraction?

Absolutely! Fractions can have decimals in the numerator. $ \frac{3.1}{100} $ is a perfectly valid fraction that represents exactly 3.1%.

Q: How do I convert this back to check my work?

Divide the numerator by denominator: 3.1 ÷ 100 = 0.031. Then multiply by 100 to get the percentage: 0.031 × 100 = 3.1% ✓

Q: What if the percentage has more decimal places?

The same rule applies! For example, 2.75% = $ \frac{2.75}{100} $. Just keep the exact decimal in the numerator and 100 in the denominator.

Percentage to Fraction with Decimal Values

Write the percentage 3.1% as a fraction with a denominator of 100.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert from percentages to fractions

00:05 The percentage equals a fraction where the numerator is the percentage (X) and the denominator is 100

00:10 Apply this formula to our exercise

00:22 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Write the percentage 3.1% as a fraction with a denominator of 100.

Step-by-step solution

To solve this problem, we'll convert 3.1% into a fraction with denominator of 100 following these steps:

Identify the given percentage: 3.1%
Use the conversion method for percentages: Convert the percentage to a fraction by dividing the percentage by 100. Specifically, $3.1\%$ is converted as follows:

Step: Convert the percentage to a fraction:

$3.1\% = \frac{3.1}{100}$

Therefore, the solution to the problem is $\frac{3.1}{100}$

Thus, the correct choice from the given options is:

Choice 2: $\frac{3.1}{100}$

This matches the correct answer provided initially.

Final Answer

$\frac{3.1}{100}$

Key Points to Remember

Essential concepts to master this topic

Percentage Rule: Any percentage equals that number divided by 100
Technique: Keep decimal in numerator: 3.1% = $\frac{3.1}{100}$
Check: Convert back: $\frac{3.1}{100} = 0.031 = 3.1\%$ ✓

Common Mistakes

Avoid these frequent errors

Converting decimal percentages to whole numbers in the numerator
Don't change 3.1% to $\frac{31}{100}$ = 31%! This multiplies the original value by 10 and gives a completely wrong answer. Always keep the decimal exactly as given: 3.1% = $\frac{3.1}{100}$ .

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 can't I just remove the decimal and write 31/100?

Because 3.1 and 31 are different numbers! When you write $\frac{31}{100}$ , you're saying 31%, which is 10 times bigger than 3.1%. Always keep decimals exactly as they appear.

Is it okay to have a decimal in the numerator of a fraction?

Absolutely! Fractions can have decimals in the numerator. $\frac{3.1}{100}$ is a perfectly valid fraction that represents exactly 3.1%.

Should I simplify this fraction further?

The question specifically asks for a denominator of 100, so $\frac{3.1}{100}$ is the exact answer required. Don't change the denominator!

How do I convert this back to check my work?

Divide the numerator by denominator: 3.1 ÷ 100 = 0.031. Then multiply by 100 to get the percentage: 0.031 × 100 = 3.1% ✓

What if the percentage has more decimal places?

The same rule applies! For example, 2.75% = $\frac{2.75}{100}$ . Just keep the exact decimal in the numerator and 100 in the denominator.

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