Compare Decimals: Is 0.505 Equal to 0.5005?

Q: Why aren't 0.505 and 0.5005 the same if they have similar digits?

The position of each digit matters! In $ 0.505 $, the last 5 is in the thousandths place, but in $ 0.5005 $, it's in the ten-thousandths place. Different positions mean different values.

Q: What if I add zeros to make them the same length?

Great strategy! Write them as $ 0.5050 $ and $ 0.5005 $. Now you can clearly see that 5050 ≠ 5005 in the decimal parts, so they're not equal.

Q: Does the number of decimal places always matter?

Yes! More decimal places often mean more precision. $ 0.5005 $ is more precise than $ 0.505 $ because it specifies the ten-thousandths place.

Q: Can I convert these to fractions to compare?

Absolutely! $ 0.505 = \frac{505}{1000} $ and $ 0.5005 = \frac{5005}{10000} $. Cross-multiplying: 505 × 10000 ≠ 5005 × 1000, confirming they're not equal.

Decimal Comparison with Place Value Analysis

Are the fractions equal?

$0.505 \stackrel{?}{=} 0.5005$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Are the fractions equal?

$0.505 \stackrel{?}{=} 0.5005$

Step-by-step solution

To determine if the fractions are equal, we compare the decimal numbers carefully.

In $0.505$ , the digits are 0, 5, 0, and 5.

In $0.5005$ , the digits are 0, 5, 0, 0, and 5.

The first fraction, $0.505$ , has no digit in the thousandths place, whereas the second fraction, $0.5005$ , has a zero in the thousandths place.

Therefore, $0.505 \neq 0.5005$ .

Final Answer

$\neq$

Key Points to Remember

Essential concepts to master this topic

Place Value Rule: Each decimal position has a specific value and meaning
Technique: Compare digit by digit from left to right: 0.505 vs 0.5005
Check: Count decimal places and align positions: 3 places ≠ 4 places ✓

Common Mistakes

Avoid these frequent errors

Ignoring trailing zeros in decimal comparison
Don't assume 0.505 equals 0.5005 because they look similar = wrong conclusion! The extra zero in the thousandths place makes these different values (0.505 = 505/1000 vs 0.5005 = 5005/10000). Always examine each decimal place carefully from left to right.

Practice Quiz

Test your knowledge with interactive questions

Are they the same numbers?

$0.23\stackrel{?}{=}0.32$

FAQ

Everything you need to know about this question

Why aren't 0.505 and 0.5005 the same if they have similar digits?

The position of each digit matters! In $0.505$ , the last 5 is in the thousandths place, but in $0.5005$ , it's in the ten-thousandths place. Different positions mean different values.

How can I tell which decimal is larger?

Compare from left to right, position by position. Both start with 0.50, but $0.505$ has 5 in the thousandths place while $0.5005$ has 0, making 0.505 larger.

What if I add zeros to make them the same length?

Great strategy! Write them as $0.5050$ and $0.5005$ . Now you can clearly see that 5050 ≠ 5005 in the decimal parts, so they're not equal.

Does the number of decimal places always matter?

Yes! More decimal places often mean more precision. $0.5005$ is more precise than $0.505$ because it specifies the ten-thousandths place.

Can I convert these to fractions to compare?

Absolutely! $0.505 = \frac{505}{1000}$ and $0.5005 = \frac{5005}{10000}$ . Cross-multiplying: 505 × 10000 ≠ 5005 × 1000, confirming they're not equal.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Decimal Fractions - Basic questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime