Compare Decimals 1.3 and 1.02: Number Line Inequality Problem

Q: Why is 1.3 greater than 1.02 if 1.02 has more numbers?

The number of digits doesn't matter in decimals! What matters is place value. 1.3 means 1 and 3 tenths, while 1.02 means 1 and 2 hundredths. Since 3 tenths = 30 hundredths, we have 30 > 2.

Q: How do I use the number line to compare decimals?

On a number line, numbers get larger as you move right. Find both decimals on the line - whichever is farther to the right is the larger number. The number line shows 1.3 is right of 1.02.

Q: Should I add zeros to make decimals the same length?

Adding zeros helps but isn't required! $ 1.3 = 1.30 $ makes it easier to compare with 1.02. Now you can see 30 hundredths vs 2 hundredths clearly.

Q: What if the whole number parts are different?

Always compare the whole number part first! If one whole number is bigger, that decimal is bigger regardless of what comes after the decimal point. Only compare decimal parts when whole numbers are equal.

Q: How can I remember which symbol to use?

Think of the symbols as arrows pointing to the smaller number: points left to smaller. Or remember: the 'mouth' of the symbol always 'eats' the bigger number!

Decimal Comparison with Place Value Analysis

Determine the appropriate sign according to the number line:

$1.3?1.02$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:07 First, let's choose the right sign for our numbers.

00:12 We'll use a number line to locate the two numbers.

00:20 Remember, if a number is to the left of another, it's smaller. If it's to the right, it's larger.

00:25 Now, let's see where our number stands compared to the second number.

00:34 And that's how we solve this problem!

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:

$1.3?1.02$

Step-by-step solution

Let's look at the number 1.3

We'll add 0 to it in order to equate with 1.02

That is:

$1.3=1.02$

Since both numbers start with 1, we'll focus on the numbers after the decimal point and discover that:

$1.30>1.02$

Final Answer

$>$

Key Points to Remember

Essential concepts to master this topic

Rule: Compare decimals by aligning place values from left to right
Technique: Add zeros to match decimal places: 1.30 vs 1.02
Check: Verify on number line: 1.3 is farther right than 1.02 ✓

Common Mistakes

Avoid these frequent errors

Comparing decimal length instead of place value
Don't assume 1.02 > 1.3 because 1.02 has more digits = wrong comparison! Length doesn't determine size in decimals. Always align place values: 1.30 > 1.02 because 3 tenths > 0 tenths.

Practice Quiz

Test your knowledge with interactive questions

Which decimal number is greater?

FAQ

Everything you need to know about this question

Why is 1.3 greater than 1.02 if 1.02 has more numbers?

The number of digits doesn't matter in decimals! What matters is place value. 1.3 means 1 and 3 tenths, while 1.02 means 1 and 2 hundredths. Since 3 tenths = 30 hundredths, we have 30 > 2.

How do I use the number line to compare decimals?

On a number line, numbers get larger as you move right. Find both decimals on the line - whichever is farther to the right is the larger number. The number line shows 1.3 is right of 1.02.

Should I add zeros to make decimals the same length?

Adding zeros helps but isn't required! $1.3 = 1.30$ makes it easier to compare with 1.02. Now you can see 30 hundredths vs 2 hundredths clearly.

What if the whole number parts are different?

Always compare the whole number part first! If one whole number is bigger, that decimal is bigger regardless of what comes after the decimal point. Only compare decimal parts when whole numbers are equal.

How can I remember which symbol to use?

Think of the symbols as arrows pointing to the smaller number: < points left to smaller, > points left to smaller. Or remember: the 'mouth' of the symbol always 'eats' the bigger number!

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