Decimal Comparison: Find the Missing Sign Between 0.2 and 0.3

Q: Why isn't 0.2 greater than 0.3 since 2 is bigger than 3?

Great question! In decimals, the position matters more than the digit itself. Both 2 and 3 are in the tenths place, so we compare them directly: 2 tenths

Q: How can I remember which way the symbols point?

Think of the symbol as a hungry mouth that always wants to eat the bigger number! The open side faces the larger number: \( 0.2

Q: What if the decimals had different numbers of digits?

No problem! You can add zeros to make them the same length. For example, $ 0.2 = 0.20 $ and $ 0.3 = 0.30 $, then compare: \( 0.20

Q: Can I use a number line to help me compare?

Absolutely! On a number line, numbers get bigger as you move right. Since 0.2 is to the left of 0.3, we know \( 0.2

Q: What's the difference between < and ≤?

Great observation! The symbol "less than" (not equal), while ≤ means "less than or equal to". Since 0.2 ≠ 0.3, we use the regular

Decimal Comparison with Single Digit Tenths

Fill in the missing sign:

$0.2?0.3$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Complete the appropriate sign

00:07 Convert decimal fraction to simple fraction

00:20 To move the decimal point once, divide by 10

00:32 Place the fraction in the equation

00:40 We'll also convert this decimal fraction to a simple fraction

00:50 To move the decimal point once, divide by 10

01:02 Place the fraction and compare

01:12 In fractions with equal denominators, the larger numerator is greater

01:20 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:

$0.2?0.3$

Step-by-step solution

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

Step 1: Compare the decimal numbers based on their representation.
Step 2: Determine the correct relational sign.

Let's work through each step:

Step 1: We are given the numbers $0.2$ and $0.3$ . These numbers have one decimal place each.

The tenths digit of $0.2$ is $2$ , and the tenths digit of $0.3$ is $3$ .

Step 2: Comparing these tenths digits, we observe:

$2 \lt 3$ , which means that $0.2 \lt 0.3$ .
Therefore, the correct mathematical relation between $0.2$ and $0.3$ is the sign $\lt$ .

Hence, the correct relationship to fill in the blank is: $0.2 \lt 0.3$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Compare decimal places from left to right systematically
Technique: Look at tenths place: 2 vs 3, so 0.2 < 0.3
Check: Visualize on number line: 0.2 comes before 0.3 ✓

Common Mistakes

Avoid these frequent errors

Comparing decimal numbers like whole numbers
Don't think 0.2 > 0.3 because 2 > 3 = completely wrong answer! This ignores decimal place value. Always compare digits in the same decimal position, starting from the tenths place.

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 isn't 0.2 greater than 0.3 since 2 is bigger than 3?

Great question! In decimals, the position matters more than the digit itself. Both 2 and 3 are in the tenths place, so we compare them directly: 2 tenths < 3 tenths.

How can I remember which way the symbols point?

Think of the symbol as a hungry mouth that always wants to eat the bigger number! The open side faces the larger number: $0.2 < 0.3$

What if the decimals had different numbers of digits?

No problem! You can add zeros to make them the same length. For example, $0.2 = 0.20$ and $0.3 = 0.30$ , then compare: $0.20 < 0.30$

Can I use a number line to help me compare?

Absolutely! On a number line, numbers get bigger as you move right. Since 0.2 is to the left of 0.3, we know $0.2 < 0.3$

What's the difference between < and ≤?

Great observation! The symbol < means "less than" (not equal), while ≤ means "less than or equal to". Since 0.2 ≠ 0.3, we use the regular < symbol.

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