Convert 0.08 to Simplified Fraction Form: Step-by-Step Solution

Q: How do I know what denominator to use when converting 0.08?

Count the decimal places! Since 0.08 has 2 decimal places, use 100 (which has 2 zeros). One decimal place = 10, two decimal places = 100, three = 1000, and so on.

Q: Can I simplify by dividing by 2 multiple times instead?

Yes! $ \frac{8}{100} \div 2 = \frac{4}{50} \div 2 = \frac{2}{25} $. This works but finding the GCD (4) is faster since you divide just once.

Q: How can I check if my fraction equals the original decimal?

Divide the numerator by the denominator: $ 2 \div 25 = 0.08 $. If you get back to your original decimal, you're correct!

Q: What if the decimal has more places like 0.125?

Same process! 0.125 has 3 decimal places, so write it as $ \frac{125}{1000} $, then find the GCD and simplify. The method never changes.

Decimal to Fraction with GCD Simplification

Write 0.08 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 it to a simple and reduced fraction.

00:07 First, place the digits in the numerator.

00:11 Move the decimal point to the right until the number is a whole number.

00:15 We moved it 2 times, so the denominator is 100.

00:19 Now, let's reduce the fraction.

00:22 Break down 8 into 4 and 2, and 100 into 4 and 25.

00:28 Reduce by canceling common factors.

00:32 And there you go, that's the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Write 0.08 as a fraction and reduce.

Step-by-step solution

To solve this problem, we'll take the following steps:

Step 1: Convert the decimal to a fraction
Step 2: Simplify the fraction

Let's work through each step:

Step 1: Convert the decimal to a fraction
The decimal 0.08 can be interpreted as eight hundredths, which means it can be written as the fraction $\frac{8}{100}$ . This step uses the place value of the decimal where the hundredths place is equivalent to $\frac{1}{100}$ .

Step 2: Simplify the fraction
To simplify $\frac{8}{100}$ , we need to find the greatest common divisor (GCD) of 8 and 100. The factors of 8 are 1, 2, 4, 8, and the factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100. The greatest common factor shared by both is 4.
Divide the numerator and the denominator by the GCD, which is 4: $\frac{8 \div 4}{100 \div 4} = \frac{2}{25}$

Therefore, after converting 0.08 to a fraction and simplifying, the simplest form is $\frac{2}{25}$ .

Final Answer

$\frac{2}{25}$

Key Points to Remember

Essential concepts to master this topic

Place Value Rule: 0.08 means 8 hundredths or $\frac{8}{100}$
GCD Method: Find common factors: 8 and 100 share 1, 2, 4 (GCD = 4)
Verification: Check by division: $\frac{2}{25} = 2 \div 25 = 0.08$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to simplify the fraction completely
Don't leave $\frac{8}{100}$ as your final answer = not simplified! This gives you extra points off even though your conversion is correct. Always find the GCD and divide both numerator and denominator to get the simplest 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 when converting 0.08?

Count the decimal places! Since 0.08 has 2 decimal places, use 100 (which has 2 zeros). One decimal place = 10, two decimal places = 100, three = 1000, and so on.

What if I can't find the GCD easily?

Start by listing factors of the smaller number first. For 8: try 1, 2, 4, 8. Then check which ones also divide 100. The largest one that works is your GCD!

Can I simplify by dividing by 2 multiple times instead?

Yes! $\frac{8}{100} \div 2 = \frac{4}{50} \div 2 = \frac{2}{25}$ . This works but finding the GCD (4) is faster since you divide just once.

How can I check if my fraction equals the original decimal?

Divide the numerator by the denominator: $2 \div 25 = 0.08$ . If you get back to your original decimal, you're correct!

What if the decimal has more places like 0.125?

Same process! 0.125 has 3 decimal places, so write it as $\frac{125}{1000}$ , then find the GCD and simplify. The method never changes.

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