Convert 0.36 to a Simplified Fraction: Step-by-Step Solution

Q: How do I know what denominator to use?

Count the decimal places! One decimal place means denominator 10, two decimal places means denominator 100, and so on. Since 0.36 has 2 decimal places, use 100.

Q: What's the fastest way to find the GCD?

List the factors of both numbers or use the division method. For 36 and 100: factors of 36 are 1,2,3,4,6,9,12,18,36 and factors of 100 are 1,2,4,5,10,20,25,50,100. The greatest common factor is 4.

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

A fraction is fully simplified when the numerator and denominator have no common factors other than 1. Try to find any number that divides both - if you can't find any, you're done!

Decimal to Fraction with Simplification

Write the following decimal fraction as a simple fraction and simplify:

$0.36=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:07 Let's write this as a simple and reduced fraction.

00:11 Divide each digit after the decimal by the place value it represents.

00:16 Next, place the correct denominator underneath.

00:21 Now, reduce it by dividing both the top and bottom numbers by their greatest common factor.

00:33 And that's how we solve the problem! Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Write the following decimal fraction as a simple fraction and simplify:

$0.36=$

Step-by-step solution

Since there are two digits after the decimal point, we divide 36 by 100:

$\frac{36}{100}$

Now let's find the highest number that divides both the numerator and denominator.

In this case, the number is 4, so:

$\frac{36:4}{100:4}=\frac{9}{25}$

Final Answer

$\frac{9}{25}$

Key Points to Remember

Essential concepts to master this topic

Decimal Rule: Place digits over power of 10 based on decimal places
Technique: Two decimal places means denominator 100, so 0.36 = 36/100
Check: Verify 9/25 = 0.36 by dividing: 9 ÷ 25 = 0.36 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to simplify the fraction completely
Don't leave 36/100 as your final answer = not fully simplified! This gives you a correct but unnecessarily complex fraction. Always find the GCD and divide both numerator and denominator by it to get the simplest form.

Practice Quiz

Test your knowledge with interactive questions

Reduce the following fraction:

$$ 0.30 $$

FAQ

Everything you need to know about this question

How do I know what denominator to use?

Count the decimal places! One decimal place means denominator 10, two decimal places means denominator 100, and so on. Since 0.36 has 2 decimal places, use 100.

What's the fastest way to find the GCD?

List the factors of both numbers or use the division method. For 36 and 100: factors of 36 are 1,2,3,4,6,9,12,18,36 and factors of 100 are 1,2,4,5,10,20,25,50,100. The greatest common factor is 4.

Can I simplify in steps instead of finding the GCD?

Yes! You can divide by any common factor repeatedly. For example: $\frac{36}{100} = \frac{18}{50} = \frac{9}{25}$ by dividing by 2, then by 2 again.

How do I check if my fraction is fully simplified?

A fraction is fully simplified when the numerator and denominator have no common factors other than 1. Try to find any number that divides both - if you can't find any, you're done!

What if I get confused with the decimal places?

Remember: the number of zeros in the denominator equals the number of decimal places. 0.36 has 2 decimal places, so write it as $\frac{36}{100}$ (100 has 2 zeros).

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