Convert 118% to a Fraction with Denominator 100: Step-by-Step

Q: Why is 118% equal to 118/100?

The word percent literally means "per hundred"! So 118% means 118 per 100, which is exactly $ \frac{118}{100} $.

Q: Should I simplify 118/100 to lowest terms?

Not in this problem! The question specifically asks for denominator 100. If it asked for simplest form, then yes, you'd reduce to $ \frac{59}{50} $.

Q: How do I convert any percentage to a fraction with denominator 100?

Super easy! Just put the percentage number as the numerator and 100 as the denominator. So 75% = $ \frac{75}{100} $, 200% = $ \frac{200}{100} $, etc.

Q: What if the percentage has a decimal, like 118.5%?

You can still use the same method! 118.5% = $ \frac{118.5}{100} $. If you need to avoid decimals, multiply both parts by 10 to get $ \frac{1185}{1000} $.

Q: Is 118% the same as 1.18?

Yes! When you divide $ \frac{118}{100} $, you get 1.18. This means 118% = 1.18 in decimal form, which is greater than 1 whole.

Percentage Conversion with Denominator 100

Write the percentage 118% 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

00:05 Let's convert percentages to fractions.

00:10 Remember: A percentage is a fraction with a top number of X and a bottom number of 100.

00:16 Now, let's apply this formula to our exercise.

00:21 Here's how we find the solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Write the percentage 118% as a fraction with a denominator of 100.

Step-by-step solution

To solve this problem, we'll follow a simple conversion:

Step 1: Recognize that a percentage represents a number out of 100. Thus, 118% is equivalent to 118 out of 100.
Step 2: Apply the conversion formula: $\text{Percentage} = \frac{\text{Percentage number}}{100}$ .
Step 3: Directly convert 118% into a fraction using this formula: $\frac{118}{100}$ .

Since the problem asks for the fraction with a denominator of 100, we have arrived at the correct form.

Therefore, the fraction form of 118% with a denominator of 100 is $\frac{118}{100}$ .

Final Answer

$\frac{118}{100}$

Key Points to Remember

Essential concepts to master this topic

Rule: Any percentage equals the percentage number over 100
Technique: 118% becomes $\frac{118}{100}$ directly
Check: Convert back: $\frac{118}{100} = 118 ÷ 100 = 1.18 = 118\%$ ✓

Common Mistakes

Avoid these frequent errors

Trying to simplify the fraction when denominator 100 is required
Don't reduce $\frac{118}{100}$ to $\frac{59}{50}$ = wrong answer format! The problem specifically asks for denominator 100, not lowest terms. Always keep the denominator as 100 when the question requires it.

Practice Quiz

Test your knowledge with interactive questions

Convert the fraction into a percentage:

$\frac{24}{100}=\text{?}$

FAQ

Everything you need to know about this question

Why is 118% equal to 118/100?

The word percent literally means "per hundred"! So 118% means 118 per 100, which is exactly $\frac{118}{100}$ .

Should I simplify 118/100 to lowest terms?

Not in this problem! The question specifically asks for denominator 100. If it asked for simplest form, then yes, you'd reduce to $\frac{59}{50}$ .

How do I convert any percentage to a fraction with denominator 100?

Super easy! Just put the percentage number as the numerator and 100 as the denominator. So 75% = $\frac{75}{100}$ , 200% = $\frac{200}{100}$ , etc.

What if the percentage has a decimal, like 118.5%?

You can still use the same method! 118.5% = $\frac{118.5}{100}$ . If you need to avoid decimals, multiply both parts by 10 to get $\frac{1185}{1000}$ .

Is 118% the same as 1.18?

Yes! When you divide $\frac{118}{100}$ , you get 1.18. This means 118% = 1.18 in decimal form, which is greater than 1 whole.

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