Compare Decimals: Find the Symbol Between 3.33 and 3.330

Q: Why doesn't 3.330 equal more than 3.33?

The zero at the end is a trailing zero - it doesn't add any value! Think of it like saying "3 dollars and 33 cents" versus "3 dollars and 330 tenths of a cent" - they're the same amount.

Q: How do I compare decimals with different numbers of digits?

Make them have the same number of decimal places by adding zeros to the shorter one. Then compare digit by digit from left to right, just like whole numbers!

Q: Do I always need to add zeros when comparing decimals?

It's not required, but it really helps avoid mistakes! Adding zeros makes the comparison visual and clear - you can line up the digits perfectly.

Q: What if I see 3.33000 instead of 3.330?

Still the same value! Any number of trailing zeros after the last non-zero digit doesn't change the decimal's value. $ 3.33 = 3.330 = 3.3300 = 3.33000 $

Q: Can I remove trailing zeros from my answer?

Yes! It's actually preferred to write decimals in their simplest form without unnecessary trailing zeros, unless the problem specifically asks for a certain number of decimal places.

Decimal Comparison with Trailing Zeros

Fill in the missing sign:

$3.33\text{?}3.330$

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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:

$3.33\text{?}3.330$

Step-by-step solution

To solve this problem, we will compare the decimal numbers $3.33$ and $3.330$ .

First, let's express each number to have the same number of decimal places. The number $3.33$ can be written as $3.330$ since adding a zero at the end of the decimal portion does not change its value.

Next, we compare each digit position:

The whole number part: $3 = 3$ .
The first decimal place: $3 = 3$ .
The second decimal place: $3 = 3$ .
The third decimal place: $0 = 0$ .

Since both numbers $3.33$ (expressed as $3.330$ ) and $3.330$ are equal at each digit position, these numbers are equal.

Thus, the correct comparison sign to fill in is $=$ .

Therefore, the solution to the problem is $3.33 = 3.330$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Trailing zeros after decimals don't change the value
Technique: Add zeros to match decimal places: $3.33 = 3.330$
Check: Compare digit by digit: 3=3, 3=3, 3=3, 0=0 ✓

Common Mistakes

Avoid these frequent errors

Thinking more digits makes a number larger
Don't assume 3.330 > 3.33 just because it has more digits = wrong comparison! Trailing zeros don't add value, only show precision. Always align decimal places by adding zeros before comparing.

Practice Quiz

Test your knowledge with interactive questions

Which figure represents 0.1?

FAQ

Everything you need to know about this question

Why doesn't 3.330 equal more than 3.33?

The zero at the end is a trailing zero - it doesn't add any value! Think of it like saying "3 dollars and 33 cents" versus "3 dollars and 330 tenths of a cent" - they're the same amount.

How do I compare decimals with different numbers of digits?

Make them have the same number of decimal places by adding zeros to the shorter one. Then compare digit by digit from left to right, just like whole numbers!

Do I always need to add zeros when comparing decimals?

It's not required, but it really helps avoid mistakes! Adding zeros makes the comparison visual and clear - you can line up the digits perfectly.

What if I see 3.33000 instead of 3.330?

Still the same value! Any number of trailing zeros after the last non-zero digit doesn't change the decimal's value. $3.33 = 3.330 = 3.3300 = 3.33000$

Can I remove trailing zeros from my answer?

Yes! It's actually preferred to write decimals in their simplest form without unnecessary trailing zeros, unless the problem specifically asks for a certain number of decimal places.

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