Convert 16% to Its Decimal and Fraction Equivalents

Q: How do I find the GCD of 16 and 100?

List the factors: 16 has factors 1, 2, 4, 8, 16 and 100 has factors 1, 2, 4, 5, 10, 20, 25, 50, 100. The largest number that appears in both lists is 4, so GCD = 4.

Q: What if I can't remember how to simplify fractions?

Start by dividing both the top and bottom by small numbers like 2. Keep going until you can't divide evenly anymore. For $ \frac{16}{100} $: divide by 2 twice, then by 2 again to get $ \frac{4}{25} $!

Q: How do I check if my fraction is fully simplified?

Your fraction is fully simplified when the numerator and denominator share no common factors except 1. Since 4 and 25 only share the factor 1, $ \frac{4}{25} $ is correct!

Q: Are there other ways to write 16%?

Yes! 16% can be written as:Fraction: $ \frac{4}{25} $ or $ \frac{16}{100} $Decimal: 0.16Ratio: 16:100 or 4:25

Percentage Conversion with Fraction Simplification

The percentage 16% 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 The percentage equals a fraction where the numerator is the percentage (X) and the denominator is 100

00:25 Breakdown 16 into factors of 4 and 4, and 100 into factors of 4 and 25

00:28 Reduce wherever possible

00:32 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The percentage 16% is equal to:

Step-by-step solution

To solve this problem, we will convert the percentage 16% into a fraction:

Step 1: Recognize that percentages are out of 100. Thus, 16% is equal to $\frac{16}{100}$ .

Step 2: Simplify the fraction $\frac{16}{100}$ to its lowest terms. To do this, find the greatest common divisor (GCD) of 16 and 100.

The GCD of 16 and 100 is 4.

Step 3: Divide both the numerator and the denominator by the GCD:

$\frac{16 \div 4}{100 \div 4} = \frac{4}{25}$

Thus, the fraction equivalent of 16% is $\frac{4}{25}$ .

Therefore, the correct choice from the options provided is $\frac{4}{25}$ , which corresponds to choice (3).

Final Answer

$\frac{4}{25}$

Key Points to Remember

Essential concepts to master this topic

Rule: Convert percentage to fraction by placing over 100
Technique: Simplify $\frac{16}{100}$ using GCD of 4 to get $\frac{4}{25}$
Check: Verify $\frac{4}{25} = 0.16 = 16\%$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to simplify the fraction to lowest terms
Don't leave your answer as $\frac{16}{100}$ = unsimplified fraction! This makes calculations harder and isn't in standard form. Always find the GCD and divide both numerator and denominator to get the simplest form.

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

How do I find the GCD of 16 and 100?

List the factors: 16 has factors 1, 2, 4, 8, 16 and 100 has factors 1, 2, 4, 5, 10, 20, 25, 50, 100. The largest number that appears in both lists is 4, so GCD = 4.

Why can't I just write 16% as a decimal?

You absolutely can! 16% = 0.16 as a decimal. But this question specifically asks for the fraction equivalent, so you need $\frac{4}{25}$ in simplest form.

What if I can't remember how to simplify fractions?

Start by dividing both the top and bottom by small numbers like 2. Keep going until you can't divide evenly anymore. For $\frac{16}{100}$ : divide by 2 twice, then by 2 again to get $\frac{4}{25}$ !

How do I check if my fraction is fully simplified?

Your fraction is fully simplified when the numerator and denominator share no common factors except 1. Since 4 and 25 only share the factor 1, $\frac{4}{25}$ is correct!

Are there other ways to write 16%?

Yes! 16% can be written as:

Fraction: $\frac{4}{25}$ or $\frac{16}{100}$
Decimal: 0.16
Ratio: 16:100 or 4:25

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