Compare Decimals 0.08 and 0.3: Number Line Sign Determination

Q: Why isn't 0.08 bigger than 0.3 when 8 is bigger than 3?

Great question! The place value matters more than the digit itself. The 8 in 0.08 is in the hundredths place, making it worth 8/100. The 3 in 0.3 is in the tenths place, making it worth 30/100. Since 30 > 8, we have 0.3 > 0.08.

Q: How can I visualize decimal comparison?

Think of decimals as money! $ 0.08 = 8¢ $ and $ 0.3 = 30¢ $. You'd rather have 30 cents than 8 cents, right? The number line shows this same relationship visually.

Q: What's the easiest way to compare any two decimals?

Line up the decimal points and compare column by column from left to right:0.08 = 0.080.3 = 0.30Now you can see 0 tenths vs 3 tenths clearly!

Q: Can I just add zeros to make comparison easier?

Absolutely! Adding zeros to the right of decimals doesn't change their value. So 0.3 = 0.30 = 0.300. This makes it much easier to compare: 0.08 vs 0.30.

Q: How do I remember which symbol to use?

Remember: the smaller number goes with the smaller side of the symbol. Since 0.08 is smaller, it gets the pointy side: \( 0.08 . Think of the symbol as a hungry alligator that wants to eat the bigger number!

Decimal Comparison with Number Line Positioning

Determine the appropriate sign according to the number line:

$0.08?0.3$

❤️ 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

00:00 Set the appropriate sign

00:03 We'll use the number line to find the 2 numbers

00:06 If the number is to the left of the second number then it's smaller, and to the right it's larger

00:09 We'll identify the position of our number in relation to the second number

00:15 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

Determine the appropriate sign according to the number line:

$0.08?0.3$

Step-by-step solution

Let's look at the number 0.08

This number is located on the number line in the range between 0 and 0.1

In other words, the numbers in this range are:

$0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09$

Therefore, the one that is larger is 0.3

$0.3>0.08$

Final Answer

$<$

Key Points to Remember

Essential concepts to master this topic

Place Value Rule: Compare digits from left to right to determine size
Technique: 0.08 has 0 tenths, while 0.3 has 3 tenths
Check: Find both decimals on number line: 0.08 is closer to 0 than 0.3 ✓

Common Mistakes

Avoid these frequent errors

Comparing only the digits after decimal point
Don't think 8 > 3 so 0.08 > 0.3! This ignores place value completely. The 8 is in hundredths place (worth 0.08) while 3 is in tenths place (worth 0.30). Always compare place values from left to right.

Practice Quiz

Test your knowledge with interactive questions

Are they the same numbers?

$0.1\stackrel{?}{=}0.10$

FAQ

Everything you need to know about this question

Why isn't 0.08 bigger than 0.3 when 8 is bigger than 3?

Great question! The place value matters more than the digit itself. The 8 in 0.08 is in the hundredths place, making it worth 8/100. The 3 in 0.3 is in the tenths place, making it worth 30/100. Since 30 > 8, we have 0.3 > 0.08.

How can I visualize decimal comparison?

Think of decimals as money! $0.08 = 8¢$ and $0.3 = 30¢$ . You'd rather have 30 cents than 8 cents, right? The number line shows this same relationship visually.

What's the easiest way to compare any two decimals?

Line up the decimal points and compare column by column from left to right:

0.08 = 0.08
0.3 = 0.30

Now you can see 0 tenths vs 3 tenths clearly!

Can I just add zeros to make comparison easier?

Absolutely! Adding zeros to the right of decimals doesn't change their value. So 0.3 = 0.30 = 0.300. This makes it much easier to compare: 0.08 vs 0.30.

How do I remember which symbol to use?

Remember: the smaller number goes with the smaller side of the symbol. Since 0.08 is smaller, it gets the pointy side: $0.08 < 0.3$ . Think of the symbol as a hungry alligator that wants to eat the bigger number!

🌟 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