Comparing Decimal Numbers: Finding the Larger Value

Decimal Comparison with Place Value Analysis

Which decimal number is greater?

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Step-by-step video solution

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00:03 Which number is bigger?
00:07 Let's compare the digits in each number.
00:11 Look at the digit two. It's bigger than the digit one, so this number is larger.
00:17 And that's how you find out which number is bigger.

Step-by-step written solution

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1

Understand the problem

Which decimal number is greater?

2

Step-by-step solution

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

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

0.15=15100 0.15=\frac{15}{100}

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

0.2=210 0.2=\frac{2}{10}

Let's finally compare the numbers in the denominator to determine our answer:

15100>210 \frac{15}{100}>\frac{2}{10}

Therefore, the larger number is 0.15.

3

Final Answer

0.2 0.2

Key Points to Remember

Essential concepts to master this topic
  • Rule: Compare decimal numbers by aligning place values properly
  • Technique: Add zeros to match decimal places: 0.2 = 0.20
  • Check: Convert to fractions: 20100>15100 \frac{20}{100} > \frac{15}{100} confirms 0.2 > 0.15 ✓

Common Mistakes

Avoid these frequent errors
  • Comparing decimal numbers like whole numbers
    Don't think 0.15 > 0.2 because 15 > 2 = wrong comparison! This ignores place value completely. Always align decimal places first: 0.20 vs 0.15 shows 0.2 is larger.

Practice Quiz

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Which decimal number is greater?

FAQ

Everything you need to know about this question

Why does 0.2 look smaller than 0.15 if it has fewer digits?

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More digits after the decimal point doesn't mean a larger number! Think of it like money: 0.20(20cents)ismorethan0.20 (20 cents) is more than 0.15 (15 cents), even though 15 has more digits than 2.

How can I make comparing decimals easier?

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Add trailing zeros to make the same number of decimal places. Compare 0.20 vs 0.15 instead of 0.2 vs 0.15. Now you can see that 20 hundredths > 15 hundredths!

Should I always convert decimals to fractions to compare them?

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Not always! Converting to fractions works well, but aligning place values is usually faster. Use whichever method feels more comfortable to you.

What if the decimals have different numbers of decimal places?

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No problem! Just add zeros to the shorter decimal. For example: 0.7 vs 0.603 becomes 0.700 vs 0.603, making comparison much clearer.

Can I use a number line to compare decimals?

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Absolutely! Plot both numbers on a number line. The number further to the right is always larger. This visual method helps build intuition about decimal size.

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