Decimal Comparison: Determining the Greater Value Between Two Numbers

Q: Why convert to fractions when I can just compare decimals directly?

Converting to fractions helps you understand why one decimal is bigger! When both have the same denominator like $ \frac{68}{100} $ and $ \frac{88}{100} $, you just compare 68 vs 88.

Q: Can I use this method for any decimal comparison?

Absolutely! Whether comparing 0.5 vs 0.05 or 3.14 vs 3.41, convert to fractions with the same denominator or align decimal points and compare digit by digit.

Decimal Comparison with Fractional Conversion

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

00:07 The digit 8 is greater than 6, therefore this number is bigger

00:10 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

Firstly let's convert the decimal numbers into simple fractions and compare them:

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

$0.68=\frac{68}{100}$

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

$0.88=\frac{88}{100}$

Now let's compare the numbers in the numerator:

$\frac{88}{100}>\frac{68}{100}$

Therefore, the larger number is 0.88.

Final Answer

$0.88$

Key Points to Remember

Essential concepts to master this topic

Rule: Compare decimals by converting to fractions with same denominator
Technique: Convert 0.68 to 68/100 and 0.88 to 88/100
Check: Compare numerators: 88 > 68, so 0.88 > 0.68 ✓

Common Mistakes

Avoid these frequent errors

Comparing only the first digit after decimal point
Don't just look at 0.6 vs 0.8 and ignore second digits = wrong comparison! You might think 0.68 > 0.61 is wrong. Always compare all decimal places 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 to fractions when I can just compare decimals directly?

Converting to fractions helps you understand why one decimal is bigger! When both have the same denominator like $\frac{68}{100}$ and $\frac{88}{100}$ , you just compare 68 vs 88.

What if the decimals have different numbers of digits?

Add zeros to make them the same length! For example, compare 0.7 and 0.68 by writing 0.70 and 0.68, then convert: $\frac{70}{100} > \frac{68}{100}$

Is there a faster way than converting to fractions?

Yes! Line up the decimal points and compare digit by digit from left to right. Since 0.88 vs 0.68, and 8 > 6 in the tenths place, 0.88 is greater.

What if both decimals start with the same digit?

Keep comparing! For 0.67 vs 0.68, both start with 6 in tenths place, but 8 > 7 in hundredths place, so 0.68 is greater.

Can I use this method for any decimal comparison?

Absolutely! Whether comparing 0.5 vs 0.05 or 3.14 vs 3.41, convert to fractions with the same denominator or align decimal points and compare digit by digit.

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