Mathematical Analysis: Which Decimal Shows Greater Magnitude?

Decimal Comparison with Fraction Conversion

Determine 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
00:09 The digit 3 is bigger than 2, therefore this number is bigger
00:13 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

Determine which decimal number is greater:

2

Step-by-step solution

Firstly, let's convert the decimal numbers into simple fractions and compare them:

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

0.32=32100 0.32=\frac{32}{100}

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

0.33=33100 0.33=\frac{33}{100}

Now let's compare the numbers in the numerator:

33100>32100 \frac{33}{100}>\frac{32}{100}

Therefore, the larger number is 0.33.

3

Final Answer

0.33 0.33

Key Points to Remember

Essential concepts to master this topic
  • Rule: Compare decimals by aligning decimal points and digits
  • Technique: Convert to fractions: 0.33 = 33/100, 0.32 = 32/100
  • Check: Verify 33 > 32, so 33/100 > 32/100, therefore 0.33 > 0.32 ✓

Common Mistakes

Avoid these frequent errors
  • Comparing only the last digit without considering place value
    Don't just look at 3 vs 2 in the hundredths place without considering the whole number = wrong comparison! This ignores that both decimals have the same tenths digit (3). Always compare digit by digit from left to right after the decimal point.

Practice Quiz

Test your knowledge with interactive questions

Are they the same numbers?

\( 0.23\stackrel{?}{=}0.32 \)

FAQ

Everything you need to know about this question

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

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Converting to fractions like 33100 \frac{33}{100} and 32100 \frac{32}{100} makes the comparison crystal clear! You can easily see that 33 > 32, so the first decimal is larger.

What if the decimals have different numbers of digits?

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Add zeros to make them the same length! For example, compare 0.3 and 0.32 by writing 0.30 and 0.32. Now you can see that 30 < 32, so 0.30 < 0.32.

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. For 0.33 vs 0.32: both have 3 in tenths place, but 3 > 2 in hundredths place, so 0.33 is greater.

Do I always divide by 100 when converting decimals to fractions?

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Not always! The denominator depends on decimal places:

  • 1 decimal place → divide by 10
  • 2 decimal places → divide by 100
  • 3 decimal places → divide by 1000

What if I get confused about which decimal is bigger?

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Use the number line trick! Imagine both decimals on a number line - the one further to the right is always greater. Or think: "Which would you rather have as dollars? $0.33 or $0.32?"

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