Convert Decimal to Fraction: Expressing 0.15 as a Simplified Fraction

Q: Why is the denominator 100 and not 10?

Count the decimal places! 0.15 has two decimal places (the 1 and the 5). Two decimal places means the denominator is $ 10^2 = 100 $.

Q: Should I simplify the fraction further?

Yes, you can! $ \frac{15}{100} $ can be simplified to $ \frac{3}{20} $ by dividing both numerator and denominator by 5. However, both forms are correct.

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

Same rule applies! Count the decimal places: 0.125 has three places, so it becomes $ \frac{125}{1000} $. The denominator is always $ 10^n $ where n is the number of decimal places.

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

Simply divide the numerator by the denominator: $ \frac{15}{100} = 15 ÷ 100 = 0.15 $. If you get back your original decimal, you're correct!

Q: What about decimals that start with zero like 0.05?

No problem! 0.05 has two decimal places, so it's $ \frac{5}{100} $. The leading zero doesn't count as a decimal place - only count the digits after the decimal point.

Decimal to Fraction with Powers of Ten

Convert 0.15 into a fraction.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert to a simple fraction

00:03 Move the decimal point right until the number is whole

00:06 In a decimal fraction, the denominator must be some multiple of 10 by 10

00:09 We moved the point 2 places right, so we'll add 2 zeros to the denominator

00:12 Write the digits in the numerator

00:15 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Convert 0.15 into a fraction.

Step-by-step solution

To convert the decimal 0.15 into a fraction, we will follow these steps:

Step 1: Identify the decimal places
The number 0.15 has two decimal places.
Step 2: Express the decimal as a fraction with a denominator of a power of 10
Since there are two decimal places, we write 0.15 as $\frac{15}{100}$ .
Step 3: Compare with given choices
Among the provided choices, $\frac{15}{100}$ matches the initial conversion of the decimal without simplification.

Therefore, the solution to the problem in the context of the choices provided is $\frac{15}{100}$ .

Final Answer

$\frac{15}{100}$

Key Points to Remember

Essential concepts to master this topic

Rule: Count decimal places to determine denominator power of ten
Technique: Two decimal places means denominator is 100: 0.15 = $\frac{15}{100}$
Check: Divide numerator by denominator: 15 ÷ 100 = 0.15 ✓

Common Mistakes

Avoid these frequent errors

Using wrong power of ten for denominator
Don't count incorrectly and use 10 or 1000 for 0.15 = wrong fraction! The decimal 0.15 has exactly two decimal places, so the denominator must be 100. Always count decimal places carefully to get the correct power of ten.

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

Why is the denominator 100 and not 10?

Count the decimal places! 0.15 has two decimal places (the 1 and the 5). Two decimal places means the denominator is $10^2 = 100$ .

Should I simplify the fraction further?

Yes, you can! $\frac{15}{100}$ can be simplified to $\frac{3}{20}$ by dividing both numerator and denominator by 5. However, both forms are correct.

What if the decimal has more places like 0.125?

Same rule applies! Count the decimal places: 0.125 has three places, so it becomes $\frac{125}{1000}$ . The denominator is always $10^n$ where n is the number of decimal places.

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

Simply divide the numerator by the denominator: $\frac{15}{100} = 15 ÷ 100 = 0.15$ . If you get back your original decimal, you're correct!

What about decimals that start with zero like 0.05?

No problem! 0.05 has two decimal places, so it's $\frac{5}{100}$ . The leading zero doesn't count as a decimal place - only count the digits after the decimal point.

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