Decimal Comparison: Determining the Greater Value Between Two Numbers

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
1

Understand the problem

Which decimal number is greater?

2

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=68100 0.68=\frac{68}{100}

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

0.88=88100 0.88=\frac{88}{100}

Now let's compare the numbers in the numerator:

88100>68100 \frac{88}{100}>\frac{68}{100}

Therefore, the larger number is 0.88.

3

Final Answer

0.88 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

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Which decimal number is greater?

FAQ

Everything you need to know about this question

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

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Converting to fractions helps you understand why one decimal is bigger! When both have the same denominator like 68100 \frac{68}{100} and 88100 \frac{88}{100} , you just compare 68 vs 88.

What if the decimals have different numbers of digits?

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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: 70100>68100 \frac{70}{100} > \frac{68}{100}

Is there a faster way than converting to fractions?

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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?

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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?

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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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