Mathematical Comparison: Which Decimal is Greater?

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
00:15 The digit 7 is bigger than 0, so this number is bigger
00:21 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

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

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

0.77=77100 0.77=\frac{77}{100}

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

0.7=710 0.7=\frac{7}{10}

Let's compare the numbers in the numerator:

77100>710 \frac{77}{100}>\frac{7}{10}

Therefore, the larger number is 0.77.

3

Final Answer

0.77 0.77

Key Points to Remember

Essential concepts to master this topic
  • Rule: Compare decimals by aligning place values or converting to fractions
  • Technique: Convert 0.7=70100 0.7 = \frac{70}{100} and 0.77=77100 0.77 = \frac{77}{100}
  • Check: Verify by adding zeros: 0.70 vs 0.77 shows 77 > 70 ✓

Common Mistakes

Avoid these frequent errors
  • Thinking more digits always means smaller value
    Don't assume 0.7 > 0.77 because 7 > 77 = wrong comparison! You're comparing whole numbers instead of decimal values. Always align decimal places or convert to equivalent fractions with same denominators.

Practice Quiz

Test your knowledge with interactive questions

Which decimal number is greater?

FAQ

Everything you need to know about this question

Why isn't 0.7 bigger than 0.77 since 7 is bigger than 77?

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You're thinking of whole numbers, not decimals! In decimals, 0.7 means 7 tenths while 0.77 means 77 hundredths. Convert to compare: 0.7=70100 0.7 = \frac{70}{100} and 0.77=77100 0.77 = \frac{77}{100} , so 77 > 70.

What's the easiest way to compare decimals with different numbers of digits?

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Add trailing zeros to make them the same length! Compare 0.70 vs 0.77 - now you can clearly see that 70 hundredths < 77 hundredths.

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

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No! The decimal point changes everything. Without it, you'd compare 7 vs 77, but with the decimal point, you're comparing 0.7 vs 0.77, which is completely different.

How do I convert decimals to fractions for comparison?

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Count the decimal places:

  • 1 decimal place → divide by 10
  • 2 decimal places → divide by 100
  • 3 decimal places → divide by 1000
So 0.7 = 710 \frac{7}{10} and 0.77 = 77100 \frac{77}{100}

Is there a quick mental trick for decimal comparison?

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Yes! Line up the decimal points and add zeros to make equal lengths. Then compare digit by digit from left to right, just like counting: 0.70 vs 0.77 → 7 = 7, then 0 < 7, so 0.70 < 0.77.

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