Compare Decimals: Determining the Relationship Between 0.12 and 0.3

Q: Why can I add a zero to 0.3 to make it 0.30?

Adding zeros to the right of a decimal doesn't change its value! $ 0.3 = 0.30 = 0.300 $ because the zero in the hundredths place means zero hundredths.

Q: How do I know which decimal is bigger when they have different lengths?

Make them the same length by adding zeros to the shorter one. Then compare digit by digit from left to right, starting with the tenths place.

Q: What does the number line show me?

The number line shows that 0.3 is to the right of where 0.12 would be. Numbers get larger as you move right, so 0.3 > 0.12.

Q: Can I just compare 12 and 3 to decide which decimal is bigger?

No! You must consider place value. The 3 in 0.3 is in the tenths place (worth 0.3), while 12 in 0.12 represents 1 tenth + 2 hundredths (worth 0.12).

Q: How do I remember which symbol means 'less than'?

Think of the symbol as an arrow pointing to the smaller number. The wide opening faces the larger number: \( 0.12 means 0.12 is smaller.

Decimal Comparison with Visual Number Line

Determine the appropriate sign (?) according to the number line:

$0.12?0.3$

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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

00:12 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:

$0.12?0.3$

Step-by-step solution

Let's first look at the number 0.3.

We will add a 0 on the end so we can better compare it to 0.12:

$0.3=0.30$

Now, if we look at the numbers after the decimal point, we can observe that:

$0.12<0.30$

Final Answer

$<$

Key Points to Remember

Essential concepts to master this topic

Rule: Compare decimal places from left to right systematically
Technique: Add trailing zeros: 0.3 = 0.30 to compare with 0.12
Check: Verify position on number line: 0.12 is left of 0.30 ✓

Common Mistakes

Avoid these frequent errors

Comparing only the number of decimal places
Don't think 0.12 > 0.3 because 12 > 3 in the decimal digits = wrong comparison! This ignores place value where tenths are worth more than hundredths. Always align decimal places by adding zeros: 0.30 vs 0.12.

Practice Quiz

Test your knowledge with interactive questions

Which decimal number is greater?

FAQ

Everything you need to know about this question

Why can I add a zero to 0.3 to make it 0.30?

Adding zeros to the right of a decimal doesn't change its value! $0.3 = 0.30 = 0.300$ because the zero in the hundredths place means zero hundredths.

How do I know which decimal is bigger when they have different lengths?

Make them the same length by adding zeros to the shorter one. Then compare digit by digit from left to right, starting with the tenths place.

What does the number line show me?

The number line shows that 0.3 is to the right of where 0.12 would be. Numbers get larger as you move right, so 0.3 > 0.12.

Can I just compare 12 and 3 to decide which decimal is bigger?

No! You must consider place value. The 3 in 0.3 is in the tenths place (worth 0.3), while 12 in 0.12 represents 1 tenth + 2 hundredths (worth 0.12).

How do I remember which symbol means 'less than'?

Think of the symbol as an arrow pointing to the smaller number. The wide opening faces the larger number: $0.12 < 0.3$ means 0.12 is smaller.

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