Decimal Number Comparison: Identifying the Greater Value

Decimal Comparison with Fraction 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
00:08 The digit 5 is bigger than 3, therefore this number is bigger
00:11 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:

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

0.3=310 0.3=\frac{3}{10}

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

0.5=510 0.5=\frac{5}{10}

Let's now compare the numbers in the denominator:

510>310 \frac{5}{10}>\frac{3}{10}

Therefore, the larger number is 0.5.

3

Final Answer

0.5 0.5

Key Points to Remember

Essential concepts to master this topic
  • Rule: Convert decimals to fractions for easier comparison
  • Technique: Transform 0.3 to 310 \frac{3}{10} and 0.5 to 510 \frac{5}{10}
  • Check: Compare numerators when denominators are equal: 5 > 3 ✓

Common Mistakes

Avoid these frequent errors
  • Comparing only the digits after decimal point
    Don't just look at 3 vs 5 without considering decimal place value = wrong comparison! The digit position matters crucially in decimals. Always convert to fractions or align decimal places for accurate comparison.

Practice Quiz

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Which decimal number is greater?

FAQ

Everything you need to know about this question

Can I compare 0.3 and 0.5 without converting to fractions?

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Yes! You can compare directly since both have the same number of decimal places. Just compare digit by digit: 0.5 > 0.3 because 5 > 3 in the tenths place.

What if the decimals have different numbers of digits?

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Add zeros to make them equal length! For example, compare 0.3 and 0.25 by writing them as 0.30 and 0.25, then compare: 30 > 25 in the hundredths.

Why convert to fractions when I can see 0.5 > 0.3 directly?

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Fraction conversion helps you understand why one decimal is larger. It builds stronger number sense and helps with more complex decimal comparisons later!

Do I always divide by 10 when converting decimals to fractions?

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No! The denominator depends on decimal places:

  • One decimal place → divide by 10
  • Two decimal places → divide by 100
  • Three decimal places → divide by 1000

What if I get confused about which fraction is bigger?

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When fractions have the same denominator, just compare the numerators! 510>310 \frac{5}{10} > \frac{3}{10} because 5 > 3.

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