Compare Two Decimal Numbers: Greater Than Challenge

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
00:02 Which number is larger?
00:05 Let's compare the digits in each number. Shall we?
00:10 The digit 4 is greater than 3, so this number is larger!
00:16 And that's the solution to our 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:

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

0.45=45100 0.45=\frac{45}{100}

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

0.35=35100 0.35=\frac{35}{100}

Let's now compare the numbers in the numerator:

45100>35100 \frac{45}{100}>\frac{35}{100}

Therefore, the larger number is 0.45.

3

Final Answer

0.45 0.45

Key Points to Remember

Essential concepts to master this topic
  • Rule: Compare decimals by converting to fractions with same denominator
  • Technique: Convert 0.45 to 45/100 and 0.35 to 35/100
  • Check: Compare numerators when denominators equal: 45 > 35 ✓

Common Mistakes

Avoid these frequent errors
  • Comparing only the digits after the decimal without considering place value
    Don't just compare 45 vs 35 from the decimal digits = ignoring decimal place value! This method works here by accident but fails with numbers like 0.5 vs 0.45. Always convert to fractions with the same denominator or align decimal places properly.

Practice Quiz

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Which decimal number is greater?

FAQ

Everything you need to know about this question

Why convert decimals to fractions when comparing?

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Converting to fractions with the same denominator makes comparison crystal clear! When you have 45100 \frac{45}{100} vs 35100 \frac{35}{100} , you just compare 45 vs 35.

Can I compare decimals without converting to fractions?

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Yes! You can line up the decimal points and compare digit by digit from left to right. 0.45 vs 0.35: both have 0 in ones place, but 4 > 3 in tenths place, so 0.45 is greater.

What if the decimals have different numbers of digits?

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Add trailing zeros to make them the same length! For example, 0.5 vs 0.45 becomes 0.50 vs 0.45, then convert: 50100>45100 \frac{50}{100} > \frac{45}{100} .

Why do we divide by 100 for two decimal places?

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Each decimal place represents a power of 10. Two decimal places means hundredths, so we use 100 as the denominator. Three places would use 1000, and so on.

Is there a faster way than converting to fractions?

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Yes! For decimals with the same number of places, just compare the numbers formed by all digits after the decimal. Here: 45 > 35, so 0.45 > 0.35.

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