Convert 1.8% to a Fraction: Finding the Equivalent /100 Form

Q: Why does 1.8% become 1.8/100 and not 18/100?

The % symbol already means 'divided by 100', so 1.8% literally means 1.8 ÷ 100. You don't need to move any decimal places - just write exactly what you see over 100!

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

Yes! $ \frac{1.8}{100} $ is a perfectly valid fraction. You can keep it as is, or convert to $ \frac{18}{1000} $ if you prefer whole numbers.

Q: How do I convert this to lowest terms?

To simplify $ \frac{1.8}{100} $, first convert to $ \frac{18}{1000} $, then divide both by their GCD of 2 to get $ \frac{9}{500} $.

Q: Can I write this as a mixed number?

Since 1.8 $ \frac{1.8}{100} $ is already less than 1, so it cannot be written as a mixed number. It's a proper fraction.

Q: What's the decimal form of this fraction?

Divide: 1.8 ÷ 100 = 0.018. This confirms our answer since 0.018 = 1.8% when you multiply by 100!

Percentage Conversion with Decimal Numerators

Write the percentage 1.8% 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

00:06 Let's learn how to convert percentages into fractions.

00:12 A percentage can be turned into a fraction by placing the percentage number over one hundred.

00:19 Now, let's apply this formula to our exercise.

00:24 And there you have it! That's the solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Write the percentage 1.8% as a fraction with a denominator of 100.

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Recognize that a percentage is a fraction with a denominator of 100.
Step 2: Write 1.8% as a fraction with a denominator of 100.

Now, let's work through each step:
Step 1: The percentage 1.8% is already signifying 1.8 parts out of 100. Therefore, 1.8% is equivalent to $\frac{1.8}{100}$ .
Step 2: As this matches the given condition of having the denominator as 100, no further modification is needed.

Therefore, the solution to the problem is $\frac{1.8}{100}$ .

Final Answer

$\frac{1.8}{100}$

Key Points to Remember

Essential concepts to master this topic

Rule: Any percentage equals that number over 100
Technique: Write 1.8% directly as $\frac{1.8}{100}$
Check: Verify 1.8 ÷ 100 = 0.018 = 1.8% ✓

Common Mistakes

Avoid these frequent errors

Moving decimal point incorrectly
Don't change 1.8% to 18/100 or 180/100 by moving decimal places = wrong fraction! The % symbol already means 'out of 100', so moving decimals double-counts the conversion. Always write the exact percentage number over 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 does 1.8% become 1.8/100 and not 18/100?

The % symbol already means 'divided by 100', so 1.8% literally means 1.8 ÷ 100. You don't need to move any decimal places - just write exactly what you see over 100!

Is it okay to have a decimal in the numerator?

Yes! $\frac{1.8}{100}$ is a perfectly valid fraction. You can keep it as is, or convert to $\frac{18}{1000}$ if you prefer whole numbers.

How do I convert this to lowest terms?

To simplify $\frac{1.8}{100}$ , first convert to $\frac{18}{1000}$ , then divide both by their GCD of 2 to get $\frac{9}{500}$ .

Can I write this as a mixed number?

Since 1.8 < 100, the fraction $\frac{1.8}{100}$ is already less than 1, so it cannot be written as a mixed number. It's a proper fraction.

What's the decimal form of this fraction?

Divide: 1.8 ÷ 100 = 0.018. This confirms our answer since 0.018 = 1.8% when you multiply by 100!

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