Compare Two Decimals: Finding the Larger Number

Q: Why is 0.55 bigger than 0.5 if 5 is less than 55?

You're comparing whole numbers instead of decimal values! Think of it as money: 0.5 = 50 cents and 0.55 = 55 cents. Which is more money?

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

Add zeros to the end of the shorter decimal to make them the same length. For example: 0.5 becomes 0.50, then compare 0.50 vs 0.55.

Q: Can I just ignore the decimal point and compare the numbers?

Never! The decimal point shows place value. 0.5 means 5 tenths, while 0.55 means 55 hundredths. They're completely different values.

Q: What if I convert to fractions like in the explanation?

That's a great method! Convert both to the same denominator: $ 0.5 = \frac{50}{100} $ and $ 0.55 = \frac{55}{100} $. Now compare numerators: 50

Q: Is there a faster way than converting to fractions?

Yes! Line up the decimal points and compare digit by digit from left to right. When you find the first different digit, the larger digit belongs to the larger number.

Decimal Comparison with Place Value Analysis

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 larger?

00:03 Let's compare the digits between the numbers

00:10 The digit 5 is larger than 0, therefore this number is larger

00:18 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

Which decimal number is greater?

Step-by-step solution

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

0.5 is divided by 10 because there is only one number after the decimal point, therefore:

$0.5=\frac{5}{10}$

0.55 is divided by 100 because there are two numbers after the decimal point, therefore:

$0.55=\frac{55}{100}$

Let's now compare the numbers:

$\frac{55}{100}>\frac{5}{10}$

Therefore, the larger number is 0.55.

Final Answer

$0.55$

Key Points to Remember

Essential concepts to master this topic

Rule: Compare decimals by examining digits in each place value position
Technique: Convert to same decimal places: 0.5 becomes 0.50 vs 0.55
Check: Verify by converting to fractions: $\frac{50}{100} < \frac{55}{100}$ ✓

Common Mistakes

Avoid these frequent errors

Thinking more digits means smaller number
Don't assume 0.5 > 0.55 because 5 > 55 = wrong comparison! This ignores place value completely. Always align decimal places: 0.50 vs 0.55 shows 50 hundredths < 55 hundredths.

Practice Quiz

Test your knowledge with interactive questions

Are they the same numbers?

$0.23\stackrel{?}{=}0.32$

FAQ

Everything you need to know about this question

Why is 0.55 bigger than 0.5 if 5 is less than 55?

You're comparing whole numbers instead of decimal values! Think of it as money: 0.5 = 50 cents and 0.55 = 55 cents. Which is more money?

How do I compare decimals with different numbers of digits?

Add zeros to the end of the shorter decimal to make them the same length. For example: 0.5 becomes 0.50, then compare 0.50 vs 0.55.

Can I just ignore the decimal point and compare the numbers?

Never! The decimal point shows place value. 0.5 means 5 tenths, while 0.55 means 55 hundredths. They're completely different values.

What if I convert to fractions like in the explanation?

That's a great method! Convert both to the same denominator: $0.5 = \frac{50}{100}$ and $0.55 = \frac{55}{100}$ . Now compare numerators: 50 < 55.

Is there a faster way than converting to fractions?

Yes! Line up the decimal points and compare digit by digit from left to right. When you find the first different digit, the larger digit belongs to the larger number.

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