Decimal Comparison: Find the Missing Symbol Between 0.1 and 0.4

Q: Why is 0.1 less than 0.4 when 1 is smaller than 4?

Great observation! You're absolutely right that 1 same place values. Both numbers have their digits in the tenths place: $ 0.1 = \frac{1}{10} $ and $ 0.4 = \frac{4}{10} $, so \( 0.1 .

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

No problem! You can always add zeros to make them the same length. For example, $ 0.1 $ is the same as $ 0.10 $. Then compare: 0.10 vs 0.40 - clearly 0.10

Q: Should I always start comparing from the left?

Yes, always! Start with the largest place value and work your way right. For decimals, that means: tenths, then hundredths, then thousandths, etc. Stop as soon as you find a difference.

Q: Can I use a number line to help?

Absolutely! Number lines are perfect for decimal comparison. $ 0.1 $ is closer to 0, while $ 0.4 $ is closer to 0.5. Numbers further right are always greater.

Q: What does the < symbol mean again?

The symbol means "less than." Think of it like a hungry alligator that always wants to eat the bigger number! So \( 0.1 means 0.1 is less than 0.4.

Decimal Comparison with Tenths Place

Fill in the missing sign:

$\text{0}.1?0.4$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Complete the appropriate sign

00:04 Convert decimal fraction to simple fraction

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

00:18 Place the fraction in the equation

00:28 We'll also convert this decimal fraction to a simple fraction

00:39 To move the decimal point once, divide by 10

00:47 Place the fraction and compare

00:52 In fractions with equal denominators, the larger numerator is larger

00:59 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:

$\text{0}.1?0.4$

Step-by-step solution

To solve this problem, we need to compare the two decimal numbers $0.1$ and $0.4$ .

First, we look at the tenths place of both numbers:

$0.1$ has a digit of $1$ in the tenths place.
$0.4$ has a digit of $4$ in the tenths place.

Since $4$ is greater than $1$ , it follows that $0.4$ is greater than $0.1$ . Therefore, the correct comparison is $0.1 < 0.4$ .

In terms of multiple-choice answers provided, the correct comparison sign would be $\lt$ , indicating that $0.1$ is less than $0.4$ .

Therefore, the solution to the problem is: $\text{0}.1 \lt 0.4$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Compare decimal digits starting from the leftmost place value
Technique: Look at tenths place: 0.1 has 1, 0.4 has 4
Check: Convert to fractions: 1/10 vs 4/10, so 1/10 < 4/10 ✓

Common Mistakes

Avoid these frequent errors

Comparing decimals like whole numbers
Don't think 0.4 is smaller than 0.1 because 4 comes after 1 = backwards comparison! This ignores place value completely. Always compare digit by digit from left to right, starting with 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 is 0.1 less than 0.4 when 1 is smaller than 4?

Great observation! You're absolutely right that 1 < 4. In decimals, we compare the same place values. Both numbers have their digits in the tenths place: $0.1 = \frac{1}{10}$ and $0.4 = \frac{4}{10}$ , so $0.1 < 0.4$ .

What if the decimals have different numbers of digits?

No problem! You can always add zeros to make them the same length. For example, $0.1$ is the same as $0.10$ . Then compare: 0.10 vs 0.40 - clearly 0.10 < 0.40.

Should I always start comparing from the left?

Yes, always! Start with the largest place value and work your way right. For decimals, that means: tenths, then hundredths, then thousandths, etc. Stop as soon as you find a difference.

Can I use a number line to help?

Absolutely! Number lines are perfect for decimal comparison. $0.1$ is closer to 0, while $0.4$ is closer to 0.5. Numbers further right are always greater.

What does the < symbol mean again?

The symbol < means "less than." Think of it like a hungry alligator that always wants to eat the bigger number! So $0.1 < 0.4$ means 0.1 is less than 0.4.

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