Compare Decimals: Find the Missing Sign Between 0.45 and 0.450

Q: Why doesn't the extra zero in 0.450 make it bigger?

The zero is in the thousandths place, which means zero thousandths. Adding zero of anything doesn't change the total value, just like adding 0 + 5 still equals 5!

Q: What's the difference between 0.45 and 0.405?

$ 0.45 = 45 $ hundredths, while $ 0.405 = 405 $ thousandths. Since 45 hundredths = 450 thousandths, we have $ 0.45 > 0.405 $.

Q: Can I remove trailing zeros from my answer?

Yes! $ 0.450 $ and $ 0.45 $ are the same number. You can write either form, but shorter is usually preferred unless specific decimal places are required.

Decimal Comparison with Trailing Zeros

Fill in the missing sign:

$0.45\text{ }_{—\text{ }}0.450$

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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:

$0.45\text{ }_{—\text{ }}0.450$

Step-by-step solution

Let's compare the two decimal numbers $0.45$ and $0.450$ .

1. Convert $0.45$ to the same decimal places as $0.450$ :

$0.45 = 0.450$

2. Now compare the expanded forms. Since both are numerically equal, we have:

$0.450 = 0.450$

Therefore, the missing sign is $=$ .

Final Answer

$=$

Key Points to Remember

Essential concepts to master this topic

Rule: Trailing zeros after the decimal don't change the value
Technique: Compare 0.45 and 0.450 by aligning decimal places
Check: Both numbers represent 45 hundredths, so they are equal ✓

Common Mistakes

Avoid these frequent errors

Thinking more digits means a larger number
Don't assume 0.450 > 0.45 because it has more digits = wrong comparison! In whole numbers, more digits usually means bigger, but decimals work differently. Always focus on the actual place values, not the number of digits.

Practice Quiz

Test your knowledge with interactive questions

Reduce the following fraction:

$$ 0.30 $$

FAQ

Everything you need to know about this question

Why doesn't the extra zero in 0.450 make it bigger?

The zero is in the thousandths place, which means zero thousandths. Adding zero of anything doesn't change the total value, just like adding 0 + 5 still equals 5!

How can I tell if two decimals with different lengths are equal?

Add zeros to make them the same length, then compare. For example: $0.7 = 0.70 = 0.700$ . They all represent 7 tenths!

What's the difference between 0.45 and 0.405?

$0.45 = 45$ hundredths, while $0.405 = 405$ thousandths. Since 45 hundredths = 450 thousandths, we have $0.45 > 0.405$ .

Should I always add zeros to compare decimals?

It's helpful when learning! Line up the decimal points and add zeros to make comparison easier. With practice, you'll see that place value is what really matters.

Can I remove trailing zeros from my answer?

Yes! $0.450$ and $0.45$ are the same number. You can write either form, but shorter is usually preferred unless specific decimal places are required.

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