Which Decimal is Greater: Mathematical Comparison Practice

Q: Why convert decimals to fractions when comparing?

Converting to fractions makes comparison crystal clear! When you see $ \frac{5}{10} $ vs $ \frac{4}{10} $, it's obvious that 5 > 4, so the first fraction is larger.

Q: Can I just look at the numbers after the decimal point?

Yes, but be careful! When decimals have the same number of digits (like 0.4 and 0.5), you can compare directly. But 0.4 vs 0.25 needs more careful analysis since they have different lengths.

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

Absolutely! Line up the decimal points and compare digit by digit from left to right. First different digit tells you which decimal is larger: 0.5 vs 0.4 → 5 > 4 in tenths place.

Q: Why does 0.5 equal 5/10 and not 5/100?

Count decimal places: 0.5 has 1 digit after decimal = tenths placeDenominator rule: 1 decimal place = divide by 10Result: 0.5 = 5 ÷ 10 = $ \frac{5}{10} $

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 bigger?

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

00:09 The digit 5 is bigger than 4, therefore this number is bigger

00:12 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 digit after the decimal point, therefore:

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

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

$0.4=\frac{4}{10}$

Let's then compare the numbers in the numerator:

$\frac{5}{10}>\frac{4}{10}$

Therefore, the larger number is 0.5.

Final Answer

$0.5$

Key Points to Remember

Essential concepts to master this topic

Rule: Compare decimals by aligning decimal points and place values
Technique: Convert to fractions: 0.5 = 5/10 and 0.4 = 4/10
Check: Since 5 > 4 in numerators with same denominator, 0.5 > 0.4 ✓

Common Mistakes

Avoid these frequent errors

Comparing decimals like whole numbers
Don't think 0.4 > 0.5 because 4 > 5 in whole numbers = completely wrong comparison! This ignores decimal place values where 0.5 means 5 tenths while 0.4 means 4 tenths. Always compare the actual decimal values or convert to fractions with same denominators.

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 convert decimals to fractions when comparing?

Converting to fractions makes comparison crystal clear! When you see $\frac{5}{10}$ vs $\frac{4}{10}$ , it's obvious that 5 > 4, so the first fraction is larger.

Can I just look at the numbers after the decimal point?

Yes, but be careful! When decimals have the same number of digits (like 0.4 and 0.5), you can compare directly. But 0.4 vs 0.25 needs more careful analysis since they have different lengths.

What if the decimals have different numbers of digits?

Add zeros to make them the same length! For example: 0.4 becomes 0.40, then compare 0.40 vs 0.25. Now you can see 40 hundredths > 25 hundredths.

Is there a faster way than converting to fractions?

Absolutely! Line up the decimal points and compare digit by digit from left to right. First different digit tells you which decimal is larger: 0.5 vs 0.4 → 5 > 4 in tenths place.

Why does 0.5 equal 5/10 and not 5/100?

Count decimal places: 0.5 has 1 digit after decimal = tenths place
Denominator rule: 1 decimal place = divide by 10
Result: 0.5 = 5 ÷ 10 = $\frac{5}{10}$

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