Compare Decimals: Finding the Symbol Between 0.008 and 0.08

Q: Why is 0.008 smaller than 0.08 when it has more digits?

More digits doesn't mean bigger! Think of it as 8 cents vs 80 cents. The position of digits matters more than how many there are. $ 0.08 = 80 \text{ thousandths} $ while $ 0.008 = 8 \text{ thousandths} $.

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

Add trailing zeros to make them the same length! $ 0.08 = 0.080 $. Now compare: 0.008 vs 0.080. The first different digits are 0 and 8, so 0.008

Q: What if the numbers look really close together?

Line them up by place value! Write them vertically:0.0080.080Compare column by column from left to right until you find different digits.

Q: Can I convert to fractions instead?

Yes! $ 0.008 = \frac{8}{1000} $ and $ 0.08 = \frac{80}{1000} $. Since 8 , we have 0.008

Q: How do I remember which symbol to use?

Think of the alligator mouth eating the bigger number! Since 0.08 is larger, the mouth opens toward it: \( 0.008 . The smaller number gets the pointed end.

Decimal Comparison with Place Value Analysis

Fill in the missing sign:

$0.008\text{ }_{—\text{ }}0.08$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Choose the appropriate sign

00:03 Let's compare the digits between the numbers

00:10 You can always add more 0s on the right side after the decimal point

00:16 8 is greater than 0 so this number is larger

00:20 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Fill in the missing sign:

$0.008\text{ }_{—\text{ }}0.08$

Step-by-step solution

In order to compare which is larger, we'll compare the numbers by adding 0 to 0.08 in the following way:

$0.008\text{?}0.080$

Note that before the decimal point we have 0 in both numbers

After the decimal point in both numbers we have 0

The different numbers are the following ones, 0 versus 8

Since 8 is greater than 0, the appropriate sign is:

$0.008 < 0.080$

Final Answer

$<$

Key Points to Remember

Essential concepts to master this topic

Rule: Compare digits from left to right after decimal point
Technique: Add zeros to make equal length: 0.008 vs 0.080
Check: First different digits are 0 and 8, so 0.008 < 0.080 ✓

Common Mistakes

Avoid these frequent errors

Thinking more digits means larger number
Don't assume 0.008 > 0.08 because it has more digits = wrong comparison! More decimal digits can mean a smaller number. Always align place values 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 is 0.008 smaller than 0.08 when it has more digits?

More digits doesn't mean bigger! Think of it as 8 cents vs 80 cents. The position of digits matters more than how many there are. $0.08 = 80 \text{ thousandths}$ while $0.008 = 8 \text{ thousandths}$ .

How do I compare decimals with different numbers of digits?

Add trailing zeros to make them the same length! $0.08 = 0.080$ . Now compare: 0.008 vs 0.080. The first different digits are 0 and 8, so 0.008 < 0.080.

What if the numbers look really close together?

Line them up by place value! Write them vertically:

0.008
0.080

Compare column by column from left to right until you find different digits.

Can I convert to fractions instead?

Yes! $0.008 = \frac{8}{1000}$ and $0.08 = \frac{80}{1000}$ . Since 8 < 80, we have 0.008 < 0.08. But the place value method is usually faster!

How do I remember which symbol to use?

Think of the alligator mouth eating the bigger number! Since 0.08 is larger, the mouth opens toward it: $0.008 < 0.08$ . The smaller number gets the pointed end.

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