Comparing Decimal Values: Which Number is Larger?

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
00:02 Which number is bigger?
00:06 Let's compare the digits in each number.
00:15 The digit three is larger than two, so this number is bigger.
00:21 And that's how we solve 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:

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

0.25=25100 0.25=\frac{25}{100}

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}

Now we can compare the numbers in the numerator:

25100<310 \frac{25}{100}<\frac{3}{10}

Therefore, the larger number is 0.3.

3

Final Answer

0.3 0.3

Key Points to Remember

Essential concepts to master this topic
  • Rule: Convert decimals to fractions for easier comparison
  • Technique: Convert 0.3=310 0.3 = \frac{3}{10} and 0.25=25100 0.25 = \frac{25}{100}
  • Check: Common denominators show 30100>25100 \frac{30}{100} > \frac{25}{100}

Common Mistakes

Avoid these frequent errors
  • Assuming more decimal digits means larger value
    Don't think 0.25 > 0.3 because 25 > 3 = wrong comparison! You're comparing whole numbers, not decimals. Always compare place values from left to right or convert to common denominators.

Practice Quiz

Test your knowledge with interactive questions

Which decimal number is greater?

FAQ

Everything you need to know about this question

Why can't I just compare 25 and 3 directly?

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Because decimal place value matters! In 0.25, the digits represent hundredths, while in 0.3, it represents tenths. You need to compare like place values or convert to fractions first.

Is there an easier way than converting to fractions?

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Yes! You can add zeros to make equal decimal places: 0.3 = 0.30. Now compare: 0.30 > 0.25 is much clearer!

What if I have more than two decimals to compare?

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Use the same method: either add zeros to make all decimals have the same number of places, or convert all to fractions with a common denominator.

Can I use a number line to help?

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Absolutely! Plot both numbers on a number line. The number farther to the right is always larger. 0.3 will be to the right of 0.25.

Why did the explanation use 100 as denominator for both fractions?

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To compare fractions easily, you need a common denominator. Since 310=30100 \frac{3}{10} = \frac{30}{100} , now you can directly compare 30100 \frac{30}{100} vs 25100 \frac{25}{100} .

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