Compare Decimals: Find the Missing Sign Between 0.33 and 0.303

Q: Why can I add zeros to the end of a decimal?

Adding zeros to the right of a decimal doesn't change its value! $ 0.33 = 0.330 = 0.3300 $ - they're all equal. It just helps you compare more easily.

Q: How do I know which decimal place to compare first?

Always start from the leftmost digit after the decimal point. Compare tenths first, then hundredths, then thousandths, and so on until you find a difference.

Q: What if the first few digits are the same?

Keep comparing! In $ 0.33 $ vs $ 0.303 $, the tenths are both 3, but the hundredths are different: 3 > 0, so $ 0.33 > 0.303 $.

Q: Does having more decimal places make a number bigger?

No! $ 0.9 $ is bigger than $ 0.8765 $ even though 0.8765 has more digits. Always compare the actual digit values, not the length.

Q: How can I double-check my comparison?

Convert both decimals to the same number of decimal places, then compare like whole numbers: $ 0.330 $ vs $ 0.303 $ means 330 > 303.

Decimal Comparison with Trailing Zeros

Fill in the missing sign:

$0.33\text{ }_{—\text{ }}0.303$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Fill in the missing sign:

$0.33\text{ }_{—\text{ }}0.303$

Step-by-step solution

To decide whether $0.33$ is less than, greater than, or equal to $0.303$ , align both by the decimal point:

$0.33$ can be considered as $0.330$ . Compare the numbers starting from the left:
The digit "3" after the decimal in $0.33$ is greater than "3" in $0.303$ due to the next digit in the sequence, making $0.33$ greater than $0.303$ . Thus, the sign is $>$ .

Final Answer

$>$

Key Points to Remember

Essential concepts to master this topic

Alignment Rule: Line up decimal points to compare digits position by position
Technique: Add trailing zeros: 0.33 becomes 0.330 to match 0.303
Check: Compare left to right: 0.330 vs 0.303, so 3 > 0 in hundredths ✓

Common Mistakes

Avoid these frequent errors

Comparing decimal length instead of value
Don't think 0.303 is bigger because it has more digits = wrong comparison! More decimal places doesn't mean larger value. Always align decimals and compare digit by digit from left to right.

Practice Quiz

Test your knowledge with interactive questions

Reduce the following fraction:

$$ 0.30 $$

FAQ

Everything you need to know about this question

Why can I add zeros to the end of a decimal?

Adding zeros to the right of a decimal doesn't change its value! $0.33 = 0.330 = 0.3300$ - they're all equal. It just helps you compare more easily.

How do I know which decimal place to compare first?

Always start from the leftmost digit after the decimal point. Compare tenths first, then hundredths, then thousandths, and so on until you find a difference.

What if the first few digits are the same?

Keep comparing! In $0.33$ vs $0.303$ , the tenths are both 3, but the hundredths are different: 3 > 0, so $0.33 > 0.303$ .

Does having more decimal places make a number bigger?

No! $0.9$ is bigger than $0.8765$ even though 0.8765 has more digits. Always compare the actual digit values, not the length.

How can I double-check my comparison?

Convert both decimals to the same number of decimal places, then compare like whole numbers: $0.330$ vs $0.303$ means 330 > 303.

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