Compare Decimals: Finding the Correct Symbol Between 103.22 and 103.221

Q: Why do I need to add zeros to compare decimals?

Adding trailing zeros helps you see the numbers clearly! $ 103.22 $ becomes $ 103.220 $, making it easy to compare with $ 103.221 $ digit by digit.

Q: Does adding zeros change the value of the number?

No! Adding zeros to the right of a decimal doesn't change its value. $ 103.22 = 103.220 = 103.2200 $ - they're all equal.

Q: What if the whole number parts are different?

If the numbers before the decimal point are different, you don't need to look at decimals! For example, $ 104.1 > 103.999 $ because 104 > 103.

Q: How do I compare when decimals have many different digits?

Compare digit by digit from left to right after the decimal point. Stop at the first position where digits differ - the larger digit determines which number is greater.

Q: Can I use this method for any decimal comparison?

Yes! This place value comparison method works for all decimal numbers. Just align the decimal points, add zeros if needed, and compare systematically.

Decimal Comparison with Trailing Zeros

Choose the missing sign:

$103.22~[?]~103.221$

❤️ Continue Your Math Journey!

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

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Choose the missing sign:

$103.22~[?]~103.221$

Step-by-step solution

Let's first compare the numbers in the following way:

We'll add 0 to the number 103.22 as follows:

$103.220\text{?}103.221$

Note that, before the decimal point, both numbers start with 103.

After the decimal point, there are the numbers 2 and 2.

The different numbers are the last ones: 0 versus 1.

Since 1 is greater than 0, the appropriate sign is:

$103.220 < 103.221$

Final Answer

$>$

Key Points to Remember

Essential concepts to master this topic

Rule: Add trailing zeros to make decimals same length
Technique: Compare 103.220 versus 103.221 by examining last digit
Check: Verify 0 < 1, so 103.22 < 103.221 ✓

Common Mistakes

Avoid these frequent errors

Assuming shorter decimals are smaller
Don't think 103.22 < 103.221 just because it has fewer digits = wrong reasoning! The number of decimal places doesn't determine size. Always align decimal places by adding zeros, then compare digit by digit.

Practice Quiz

Test your knowledge with interactive questions

Which decimal number is greater?

FAQ

Everything you need to know about this question

Why do I need to add zeros to compare decimals?

Adding trailing zeros helps you see the numbers clearly! $103.22$ becomes $103.220$ , making it easy to compare with $103.221$ digit by digit.

Does adding zeros change the value of the number?

No! Adding zeros to the right of a decimal doesn't change its value. $103.22 = 103.220 = 103.2200$ - they're all equal.

What if the whole number parts are different?

If the numbers before the decimal point are different, you don't need to look at decimals! For example, $104.1 > 103.999$ because 104 > 103.

How do I compare when decimals have many different digits?

Compare digit by digit from left to right after the decimal point. Stop at the first position where digits differ - the larger digit determines which number is greater.

Can I use this method for any decimal comparison?

Yes! This place value comparison method works for all decimal numbers. Just align the decimal points, add zeros if needed, and compare systematically.

🌟 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