Decimal Comparison: Finding Numbers Less Than 0.81

Q: Why is 0.801 less than 0.81 when it has more digits?

The number of digits doesn't determine size! Look at the hundredths place: 0.801 has 0 in hundredths, while 0.81 has 1 in hundredths. Since 0

Q: How do I compare decimals with different numbers of digits?

Add zeros to make them the same length! Compare 0.810 and 0.801 - now you can clearly see that 0

Q: What's the easiest way to compare these decimals?

Start from the leftmost digit and work right. When you find the first place where digits differ, the smaller digit means the smaller number!

Q: Can I just look at the last digit to compare?

No! You must compare place by place from left to right. The last digit's position determines its importance - 0.801's last digit is in thousandths, much smaller than 0.81's last digit in hundredths.

Q: Why add a zero to 0.81 instead of comparing directly?

Adding zeros makes comparison visual and clear! Writing 0.810 vs 0.801 lets you easily see that 1 > 0 in the hundredths place, so 0.810 > 0.801.

Decimal Comparison with Place Value Analysis

Determine which of the following numbers is less than $0.81$ :

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Choose the smaller number from the given number

00:04 Let's compare the digits of the numbers

00:12 The digit 0 is smaller than 1, so the number is smaller

00:17 Let's check the next number using the same method

00:21 We can see that the numbers are equal

00:24 Let's check the next number using the same method

00:31 The digit 2 is larger than 1, so the number is larger

00:36 Let's check the next number using the same method

00:45 The digit 2 is larger than 1, so the number is larger

00:51 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 which of the following numbers is less than $0.81$ :

Step-by-step solution

In order to determine which answer is correct, let's compare the answers and find out which one is less than 0.81:

Let's observe the answers:

0.801 - By adding 0 to our number we are able to easily compare 0.810 and 0.801. Given that the hundredths digit is 0 and 0 is less than 1, this is the correct answer.

0.81 - Since both numbers are equal to each other, this is not the correct answer.

0.82 - Due to the fact that the hundredths digit is 2 and 2 is greater than 1, this is not the correct answer.

0.822 - We'll add 0 to our number and compare 0.810 and 0.822. Given that the hundredths digit is 2 and 2 is greater than 1, this is not the correct answer.

Final Answer

$0.801$

Key Points to Remember

Essential concepts to master this topic

Rule: Compare digits from left to right using place value
Technique: Add zeros to compare: $0.810$ vs $0.801$
Check: Verify hundredths place: 0 < 1, so $0.801 < 0.810$ ✓

Common Mistakes

Avoid these frequent errors

Thinking more digits means larger number
Don't assume 0.822 > 0.81 just because it has more digits = wrong comparison! The position of digits matters most. Always compare place value by place value from left to right.

Practice Quiz

Test your knowledge with interactive questions

Are they the same numbers?

$0.1\stackrel{?}{=}0.10$

FAQ

Everything you need to know about this question

Why is 0.801 less than 0.81 when it has more digits?

The number of digits doesn't determine size! Look at the hundredths place: 0.801 has 0 in hundredths, while 0.81 has 1 in hundredths. Since 0 < 1, we have 0.801 < 0.81.

How do I compare decimals with different numbers of digits?

Add zeros to make them the same length! Compare 0.810 and 0.801 - now you can clearly see that 0 < 1 in the hundredths place.

What's the easiest way to compare these decimals?

Start from the leftmost digit and work right. When you find the first place where digits differ, the smaller digit means the smaller number!

Can I just look at the last digit to compare?

No! You must compare place by place from left to right. The last digit's position determines its importance - 0.801's last digit is in thousandths, much smaller than 0.81's last digit in hundredths.

Why add a zero to 0.81 instead of comparing directly?

Adding zeros makes comparison visual and clear! Writing 0.810 vs 0.801 lets you easily see that 1 > 0 in the hundredths place, so 0.810 > 0.801.

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