Converting 90% to Its Decimal and Fractional Equivalents

Q: Why do I need to write 90% as a fraction over 100?

Because percent means "per hundred"! The word percent literally means "out of 100," so 90% means 90 out of 100, which is $ \frac{90}{100} $.

Q: How do I find the greatest common divisor (GCD) quickly?

Look for common factors! Both 90 and 100 end in 0, so they're divisible by 10. You can also use prime factorization: 90 = 2×3²×5 and 100 = 2²×5², so GCD = 2×5 = 10.

Q: What if I can't simplify the fraction?

That means the numerator and denominator have no common factors except 1! Your fraction is already in simplest form. For example, $ \frac{7}{10} $ cannot be simplified further.

Q: Can I convert to decimal instead of fraction?

Yes! 90% = 90 ÷ 100 = 0.9. However, many math problems specifically ask for the fraction form, so always read the question carefully to see what format is requested.

Q: How do I check if my simplified fraction equals the original percentage?

Convert your fraction back to percentage: $ \frac{9}{10} = 9 ÷ 10 = 0.9 = 0.9 × 100\% = 90\% $ ✓. If you get the original percentage, your answer is correct!

Percentage Conversion with Fraction Simplification

The percentage 90% is equal to:

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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

00:25 Factor 90 into 9 and 10, and 100 into 10 and 10

00:30 Reduce wherever possible

00:35 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The percentage 90% is equal to:

Step-by-step solution

The solution involves converting 90% to a fraction:

Step 1: Write 90% as a fraction over 100: $\frac{90}{100}$ .
Step 2: Simplify the fraction $\frac{90}{100}$ :
- Find the greatest common divisor (GCD) of 90 and 100. The GCD is 10.
- Divide both the numerator and the denominator by the GCD (10):
- Numerator: $\frac{90}{10} = 9$
- Denominator: $\frac{100}{10} = 10$
- The simplified fraction is $\frac{9}{10}$ .

Therefore, the percentage 90% is equal to the fraction $\frac{9}{10}$ .

Final Answer

$\frac{9}{10}$

Key Points to Remember

Essential concepts to master this topic

Rule: Convert percentage by dividing by 100: 90% = 90/100
Technique: Find GCD of 90 and 100, then divide: GCD = 10
Check: Verify 9/10 = 0.9 = 90% by converting back ✓

Common Mistakes

Avoid these frequent errors

Forgetting to simplify the fraction after conversion
Don't leave your answer as 90/100 = decimal 0.9! This is not in simplest form and won't match answer choices. Always find the GCD and divide both numerator and denominator to get the simplified fraction 9/10.

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 need to write 90% as a fraction over 100?

Because percent means "per hundred"! The word percent literally means "out of 100," so 90% means 90 out of 100, which is $\frac{90}{100}$ .

How do I find the greatest common divisor (GCD) quickly?

Look for common factors! Both 90 and 100 end in 0, so they're divisible by 10. You can also use prime factorization: 90 = 2×3²×5 and 100 = 2²×5², so GCD = 2×5 = 10.

What if I can't simplify the fraction?

That means the numerator and denominator have no common factors except 1! Your fraction is already in simplest form. For example, $\frac{7}{10}$ cannot be simplified further.

Can I convert to decimal instead of fraction?

Yes! 90% = 90 ÷ 100 = 0.9. However, many math problems specifically ask for the fraction form, so always read the question carefully to see what format is requested.

How do I check if my simplified fraction equals the original percentage?

Convert your fraction back to percentage: $\frac{9}{10} = 9 ÷ 10 = 0.9 = 0.9 × 100\% = 90\%$ ✓. If you get the original percentage, your answer is correct!

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