Compare Decimals: Find the Missing Sign Between 10.04 and 10.40

Q: Why can't I just look at all the digits after the decimal?

Because place value matters! The digit 4 in the tenths place (0.4) is much larger than 4 in the hundredths place (0.04). You must compare position by position from left to right.

Q: What if one decimal has more digits than the other?

Add zeros to make them the same length! For example, $ 10.4 $ becomes $ 10.40 $. This doesn't change the value but makes comparison easier.

Q: Do I always start comparing from the left?

Yes, always! Start with the largest place value (whole numbers), then move right to tenths, hundredths, and so on. Stop as soon as you find a difference.

Q: What does it mean when the tenths place is different?

The tenths place represents one-tenth of a whole. So 0.4 means 4 tenths, while 0.0 means 0 tenths. Since 4 tenths > 0 tenths, any number with 4 in the tenths place is larger.

Q: How can I remember which symbol to use?

Think of the symbols as arrows pointing to the smaller number: \( 10.04 means the arrow points left to the smaller number (10.04).

Decimal Comparison with Place Value Analysis

Fill in the missing sign:

$10.04?10.40$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Fill in the missing sign:

$10.04?10.40$

Step-by-step solution

To solve this problem, we'll proceed as follows:

Step 1: Start by comparing the whole number part, which is the integer part before the decimal point. Both $10.04$ and $10.40$ have the integer part $10$ .
Step 2: Since the integer parts are equal, move on to compare the digits immediately following the decimal point, which are in the tenths place.
Step 3: Observe that in the tenths place, $10.04$ has a $0$ while $10.40$ has a $4$ .
Step 4: Since $0 < 4$ , we conclude that $10.04 < 10.40$ .

Therefore, we fill in the missing sign as $<$ .

Comparing all the choices, choice (1), which is "<", correctly represents the relationship between the two numbers.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Compare decimal digits from left to right by place value
Technique: When whole parts equal, check tenths: 0 vs 4 in 10.04 vs 10.40
Check: Convert to same decimal places: 10.04 = 10.04 and 10.40 = 10.40 ✓

Common Mistakes

Avoid these frequent errors

Comparing only the digits after the decimal point as whole numbers
Don't compare 04 vs 40 as if they're whole numbers = wrong conclusion that 10.04 > 10.40! This ignores place value completely. Always compare digit by digit from left to right, considering each position'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 can't I just look at all the digits after the decimal?

Because place value matters! The digit 4 in the tenths place (0.4) is much larger than 4 in the hundredths place (0.04). You must compare position by position from left to right.

What if one decimal has more digits than the other?

Add zeros to make them the same length! For example, $10.4$ becomes $10.40$ . This doesn't change the value but makes comparison easier.

Do I always start comparing from the left?

Yes, always! Start with the largest place value (whole numbers), then move right to tenths, hundredths, and so on. Stop as soon as you find a difference.

What does it mean when the tenths place is different?

The tenths place represents one-tenth of a whole. So 0.4 means 4 tenths, while 0.0 means 0 tenths. Since 4 tenths > 0 tenths, any number with 4 in the tenths place is larger.

How can I remember which symbol to use?

Think of the symbols as arrows pointing to the smaller number: $10.04 < 10.40$ means the arrow points left to the smaller number (10.04).

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