Decimal Number Comparison: Determining the Greater Value

Q: Why do we convert decimals to fractions to compare them?

Converting to fractions makes comparison crystal clear! When both decimals have the same denominator like $ \frac{24}{100} $ and $ \frac{25}{100} $, you just compare the numerators: 25 > 24.

Q: Can I compare decimals without converting to fractions?

Absolutely! Line up the decimal points and compare digit by digit from left to right. Since 0.24 and 0.25 have the same tenths digit (2), check hundredths: 5 > 4, so 0.25 > 0.24.

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

Add zeros to the right to make them equal length! For example, 0.3 vs 0.25 becomes 0.30 vs 0.25. Now compare: 30 hundredths > 25 hundredths.

Q: How can I remember which decimal is bigger?

Think of money! 0.25 is 25 cents and 0.24 is 24 cents. You'd rather have 25 cents than 24 cents, so 0.25 > 0.24.

Q: Do I always need to write fractions with 100 in the denominator?

Not always! Use the place value that matches your decimal. For 0.7 vs 0.8, use tenths: $ \frac{7}{10} $ vs $ \frac{8}{10} $. For 0.24 vs 0.25, use hundredths since both go to the hundredths place.

Decimal Comparison with Hundredths Place

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?

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

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

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 convert the decimal numbers into simple fractions and compare them:

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

$0.24=\frac{24}{100}$

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

$0.25=\frac{25}{100}$

Let's now compare the numbers in the numerator:

$\frac{25}{100}>\frac{24}{100}$

Therefore, the larger number is 0.25.

Final Answer

$0.25$

Key Points to Remember

Essential concepts to master this topic

Rule: Compare decimals by examining each place value from left to right
Technique: Convert to fractions: 0.24 = $\frac{24}{100}$ and 0.25 = $\frac{25}{100}$
Check: Since 25 > 24 in numerators with same denominator, 0.25 > 0.24 ✓

Common Mistakes

Avoid these frequent errors

Comparing only the last digit without considering place value
Don't just look at 4 vs 5 and think 0.24 > 0.25 because 4 < 5 = wrong comparison! This ignores that both digits are in the same hundredths place. Always compare the actual decimal values: 0.24 means 24 hundredths while 0.25 means 25 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 do we convert decimals to fractions to compare them?

Converting to fractions makes comparison crystal clear! When both decimals have the same denominator like $\frac{24}{100}$ and $\frac{25}{100}$ , you just compare the numerators: 25 > 24.

Can I compare decimals without converting to fractions?

Absolutely! Line up the decimal points and compare digit by digit from left to right. Since 0.24 and 0.25 have the same tenths digit (2), check hundredths: 5 > 4, so 0.25 > 0.24.

What if the decimals have different numbers of digits?

Add zeros to the right to make them equal length! For example, 0.3 vs 0.25 becomes 0.30 vs 0.25. Now compare: 30 hundredths > 25 hundredths.

How can I remember which decimal is bigger?

Think of money! 0.25 is 25 cents and 0.24 is 24 cents. You'd rather have 25 cents than 24 cents, so 0.25 > 0.24.

Do I always need to write fractions with 100 in the denominator?

Not always! Use the place value that matches your decimal. For 0.7 vs 0.8, use tenths: $\frac{7}{10}$ vs $\frac{8}{10}$ . For 0.24 vs 0.25, use hundredths since both go to the hundredths place.

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