Decimal Comparison: Find the Missing Symbol Between 0.30 and 0.3

Q: Why does 0.30 equal 0.3 if they look different?

The trailing zero in $ 0.30 $ is just a placeholder - it doesn't add any value! Think of it like $5.00 and $5 - they're the same amount of money even though one has more digits.

Q: How can I tell if two decimals are equal when they have different numbers of digits?

Add zeros to make them the same length! $ 0.3 $ becomes $ 0.30 $, then compare digit by digit from left to right. If all digits match, the numbers are equal.

Q: What's the difference between 0.3 and 0.03?

Big difference! $ 0.3 $ is three tenths, while $ 0.03 $ is three hundredths. The position of digits matters - only trailing zeros (after the last non-zero digit) don't change the value.

Decimal Equivalence with Trailing Zeros

Fill in the missing sign (?):

$0.30?0.3$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Fill in the correct sign between the numbers.

00:09 Let's turn the decimal fraction into a simple fraction.

00:22 To move the decimal point two places left, divide by one hundred.

00:35 Place this fraction into the equation now.

00:43 We'll also change this decimal fraction to a simple fraction.

00:53 To shift the decimal point one place, divide by ten.

01:06 Multiply both top and bottom numbers to find a common denominator.

01:27 Now, compare these fractions side by side.

01:37 And that's how we find the solution to our problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Fill in the missing sign (?):

$0.30?0.3$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Compare the two numbers by aligning their decimal places.
Step 2: Conclude the relationship after comparison.

Now, let's work through each step:
Step 1: The numbers are $0.30$ and $0.3$ . To compare them, convert $0.3$ to $0.30$ by adding a trailing zero. Now, both numbers have two decimal places, and the comparison is straightforward: $0.30$ vs. $0.30$ .

Step 2: With both numbers clearly written as $0.30$ , it is evident that they are equal.

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

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Trailing zeros after decimal point don't change value
Technique: Align decimal places: 0.3 = 0.30 for easy comparison
Check: Convert both to same decimal places and compare digit by digit ✓

Common Mistakes

Avoid these frequent errors

Thinking 0.30 is greater than 0.3 because it has more digits
Don't assume more digits means greater value = 0.30 > 0.3 is wrong! The extra zero doesn't add value, just like $5.00 equals $5. Always remember trailing zeros after decimals are placeholders that don't change the number's value.

Practice Quiz

Test your knowledge with interactive questions

Determine the numerical value of the shaded area:

FAQ

Everything you need to know about this question

Why does 0.30 equal 0.3 if they look different?

The trailing zero in $0.30$ is just a placeholder - it doesn't add any value! Think of it like $5.00 and $5 - they're the same amount of money even though one has more digits.

How can I tell if two decimals are equal when they have different numbers of digits?

Add zeros to make them the same length! $0.3$ becomes $0.30$ , then compare digit by digit from left to right. If all digits match, the numbers are equal.

Does 0.300 also equal 0.3?

Yes! You can add as many trailing zeros as you want after a decimal point - $0.3 = 0.30 = 0.300 = 0.3000$ and so on. They all represent the same value.

What's the difference between 0.3 and 0.03?

Big difference! $0.3$ is three tenths, while $0.03$ is three hundredths. The position of digits matters - only trailing zeros (after the last non-zero digit) don't change the value.

When comparing decimals, should I always add zeros first?

It's a great strategy! Adding zeros to make decimals the same length helps you compare them systematically. Line them up and compare digit by digit from left to right.

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