Convert 0.72 to a Reduced Fraction: Decimal Transformation

Q: How do I know what denominator to use for a decimal?

Count the decimal places! 0.72 has 2 decimal places, so use $ \frac{72}{100} $. One decimal place uses 10, two uses 100, three uses 1000, and so on.

Q: Can I simplify the fraction in steps instead of all at once?

Absolutely! You can divide by smaller common factors first. For example: $ \frac{72}{100} $ ÷ 2 = $ \frac{36}{50} $ ÷ 2 = $ \frac{18}{25} $. Just make sure you reach the lowest terms!

Q: How can I check if my fraction is fully reduced?

The fraction is fully reduced when the GCD of the numerator and denominator is 1. For $ \frac{18}{25} $, 18 and 25 share no common factors except 1, so it's fully simplified.

Q: What if the decimal has more than 2 places?

Same process! 0.375 (3 decimal places) becomes $ \frac{375}{1000} $, then find the GCD and reduce. The more decimal places, the larger the denominator, but the method stays the same.

Decimal Conversion with Greatest Common Divisor

Write 0.72 as a fraction and reduce.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's convert this into a simpler fraction. Ready?

00:07 First, put all the digits in the numerator. That's the top part.

00:12 Now, move the decimal point to the right until there's no decimal. Make the number whole!

00:18 We moved it two times, so the denominator will be one hundred.

00:22 Next, let's reduce the fraction as much as possible. Here we go!

00:27 We'll break down seventy-two into factors four and eighteen. And one hundred into four and twenty-five.

00:33 Let's simplify by reducing what we can. Almost there!

00:39 And that's how we find the solution to the question. Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Write 0.72 as a fraction and reduce.

Step-by-step solution

To convert the decimal number $0.72$ to a fraction, we need to consider the place value of the decimal.

The number $0.72$ has two decimal places. This means it can be expressed as $\frac{72}{100}$ , because the 72 is situated in the hundredths place.

Next, we need to simplify this fraction by finding the greatest common divisor (GCD) of 72 and 100. The GCD of 72 and 100 is 4. We divide both the numerator and the denominator by this GCD:

$\frac{72}{100} = \frac{72 \div 4}{100 \div 4} = \frac{18}{25}$

Thus, the fraction $\frac{18}{25}$ is the simplest form of the decimal $0.72$ .

Therefore, the solution to the problem is $\frac{18}{25}$ .

Final Answer

$\frac{18}{25}$

Key Points to Remember

Essential concepts to master this topic

Place Value: Two decimal places means denominator of 100
Technique: Find GCD of 72 and 100, which is 4
Check: Divide both numerator and denominator: 72÷4 = 18, 100÷4 = 25 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to reduce the fraction to lowest terms
Don't leave $\frac{72}{100}$ as your final answer = not fully simplified! This misses the key step of finding common factors. Always find the GCD and divide both numerator and denominator by it to get the reduced form.

Practice Quiz

Test your knowledge with interactive questions

Write the following fraction as a decimal:

$\frac{5}{100}=$

FAQ

Everything you need to know about this question

How do I know what denominator to use for a decimal?

Count the decimal places! 0.72 has 2 decimal places, so use $\frac{72}{100}$ . One decimal place uses 10, two uses 100, three uses 1000, and so on.

What's the easiest way to find the GCD of 72 and 100?

List the factors or use division! For 72 and 100: both divide by 2 twice, then by another factor. You can also use prime factorization: 72 = 2³×3², 100 = 2²×5², so GCD = 2² = 4.

Can I simplify the fraction in steps instead of all at once?

Absolutely! You can divide by smaller common factors first. For example: $\frac{72}{100}$ ÷ 2 = $\frac{36}{50}$ ÷ 2 = $\frac{18}{25}$ . Just make sure you reach the lowest terms!

How can I check if my fraction is fully reduced?

The fraction is fully reduced when the GCD of the numerator and denominator is 1. For $\frac{18}{25}$ , 18 and 25 share no common factors except 1, so it's fully simplified.

What if the decimal has more than 2 places?

Same process! 0.375 (3 decimal places) becomes $\frac{375}{1000}$ , then find the GCD and reduce. The more decimal places, the larger the denominator, but the method stays the same.

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