Which Decimal is Greater: Place Value Analysis

Decimal Comparison with Place Value Understanding

Which decimal number is greater?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Which number is bigger?
00:03 Let's compare the digits between the numbers
00:12 The digit 3 is bigger than 2, therefore this number is bigger
00:16 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Which decimal number is greater?

2

Step-by-step solution

Let's first convert the decimal numbers into simple fractions and compare them:

0.28 is divided by 100 because there are two digits after the decimal point, therefore:

0.28=28100 0.28=\frac{28}{100}

0.3 is divided by 10 because there is only one digit after the decimal point, therefore:

0.3=310 0.3=\frac{3}{10}

Let's now compare the numbers in the denominator:

28100>310 \frac{28}{100}>\frac{3}{10}

Therefore, the larger number is 0.28.

3

Final Answer

0.3 0.3

Key Points to Remember

Essential concepts to master this topic
  • Rule: Compare decimals by aligning place values from left to right
  • Technique: Convert 0.3 to 0.30 to compare with 0.28 properly
  • Check: Verify by converting to fractions: 30100>28100 \frac{30}{100} > \frac{28}{100}

Common Mistakes

Avoid these frequent errors
  • Comparing decimal digits without considering place value
    Don't think 0.28 is greater than 0.3 just because 28 > 3! This ignores place values completely. The tenths place (3) is worth more than the hundredths place (8). Always align place values: 0.30 > 0.28.

Practice Quiz

Test your knowledge with interactive questions

Which decimal number is greater?

FAQ

Everything you need to know about this question

Why isn't 0.28 bigger than 0.3 since 28 is bigger than 3?

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Great question! The key is place value. In 0.3, the 3 is in the tenths place, which means 3 tenths. In 0.28, the 8 is in the hundredths place. Since 3 tenths = 30 hundredths, we have 30 > 28!

How can I make comparing decimals easier?

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Add zeros to make the decimals have the same number of decimal places! For example, write 0.3 as 0.30. Now you can easily see that 0.30 > 0.28.

Can I convert decimals to fractions to compare them?

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Absolutely! 0.3=310=30100 0.3 = \frac{3}{10} = \frac{30}{100} and 0.28=28100 0.28 = \frac{28}{100} . Since 30100>28100 \frac{30}{100} > \frac{28}{100} , we know 0.3 > 0.28.

What if the decimals have many different places?

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Start comparing from the leftmost decimal place (tenths). If they're equal, move to the next place (hundredths), and so on. The first place where digits differ tells you which decimal is larger.

Is there a quick way to visualize this?

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Yes! Think of money: 0.3 dollars = 30 cents, while 0.28 dollars = 28 cents. You can clearly see that 30 cents > 28 cents, so 0.3 > 0.28!

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