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?

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

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Step-by-step written solution

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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

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Which decimal number is greater?

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.

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