Convert 0.27 to Fraction: Step-by-Step Decimal Conversion

Q: Why is the denominator 100 and not 10?

The denominator depends on decimal places, not digits. Since 0.27 has two decimal places, you need 10² = 100. One decimal place uses 10, two places use 100, three places use 1000.

Q: How do I know if 27/100 can be simplified?

Check if 27 and 100 share any common factors. 27 = 3 × 9 and 100 = 4 × 25. Since they share no common factors, $ \frac{27}{100} $ is already simplified!

Q: What if I wrote 270/1000 instead?

That's mathematically correct but not simplified! You added an extra zero to both numerator and denominator. $ \frac{270}{1000} = \frac{27}{100} $ when simplified.

Q: Can I check my answer by converting back to decimal?

Yes! Divide the numerator by denominator: 27 ÷ 100 = 0.27. If you get the original decimal, your fraction is correct!

Q: What's the difference between 0.27 and 0.270?

They're the same value! Adding zeros after the last decimal digit doesn't change the number's value, just like 0.27 = 0.270 = $ \frac{27}{100} $.

Decimal Conversion with Two-Place Decimals

Convert 0.27 into a fraction.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:03 First, let's convert the decimal to a simple fraction.

00:07 Move the decimal point to the right until the number becomes whole.

00:12 For decimal fractions, the denominator should be a power of ten.

00:17 We moved the point two places right, so our denominator is one hundred.

00:22 Now, write the digits without the decimal in the numerator.

00:27 And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Convert 0.27 into a fraction.

Step-by-step solution

To convert the decimal 0.27 into a fraction, follow these steps:

Step 1: Identify the number of decimal places in 0.27. There are two decimal places.
Step 2: Use a denominator of 100, since 10 to the power of 2 (the number of decimal places) is 100.
Step 3: Write the number without the decimal point as the numerator: 27.
Step 4: Write the fraction: $\frac{27}{100}$ .
Step 5: Check if the fraction can be simplified. In this case, 27 and 100 have no common factors other than 1, so the fraction $\frac{27}{100}$ is already in its simplest form.

Therefore, the decimal 0.27 as a fraction is $\frac{27}{100}$ .

Final Answer

$\frac{27}{100}$

Key Points to Remember

Essential concepts to master this topic

Rule: Count decimal places to determine denominator power of 10
Technique: Two decimal places means denominator is 100 (10²)
Check: Divide numerator by denominator: 27 ÷ 100 = 0.27 ✓

Common Mistakes

Avoid these frequent errors

Using wrong denominator based on decimal digits
Don't count the digits (2 and 7) and use 10 as denominator = 27/10 = 2.7! This ignores decimal place value. Always use 10 raised to the power of decimal places (two places = 100).

Practice Quiz

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How much of the whole does the shaded area (blue) represent?

FAQ

Everything you need to know about this question

Why is the denominator 100 and not 10?

The denominator depends on decimal places, not digits. Since 0.27 has two decimal places, you need 10² = 100. One decimal place uses 10, two places use 100, three places use 1000.

How do I know if 27/100 can be simplified?

Check if 27 and 100 share any common factors. 27 = 3 × 9 and 100 = 4 × 25. Since they share no common factors, $\frac{27}{100}$ is already simplified!

What if I wrote 270/1000 instead?

That's mathematically correct but not simplified! You added an extra zero to both numerator and denominator. $\frac{270}{1000} = \frac{27}{100}$ when simplified.

Can I check my answer by converting back to decimal?

Yes! Divide the numerator by denominator: 27 ÷ 100 = 0.27. If you get the original decimal, your fraction is correct!

What's the difference between 0.27 and 0.270?

They're the same value! Adding zeros after the last decimal digit doesn't change the number's value, just like 0.27 = 0.270 = $\frac{27}{100}$ .

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