Decimal Comparison: Is 0.22 Equal to 0.2?

Decimal Place Values with Trailing Zeros

Are they the same numbers?

0.22=?0.2 0.22\stackrel{?}{=}0.2

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:05 Are the numbers exactly the same?
00:08 Remember, we can always add zero after the last digit without changing the number.
00:14 Now, let's compare the digits in each number carefully.
00:20 Here we see, the digit two is greater than zero, which makes this number larger. So, they are not identical.
00:27 And that's how we find the solution to this question!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Are they the same numbers?

0.22=?0.2 0.22\stackrel{?}{=}0.2

2

Step-by-step solution

We will add 0 to the number 0.2 in the following way:

0.2=0.20 0.2=0.20

And we will discover that the numbers are not identical

3

Final Answer

No

Key Points to Remember

Essential concepts to master this topic
  • Rule: Trailing zeros don't change decimal value but show precision
  • Technique: Add zeros to match place values: 0.2 = 0.20
  • Check: Compare digit by digit: 0.22 has 2 hundredths, 0.20 has 0 hundredths ✓

Common Mistakes

Avoid these frequent errors
  • Thinking trailing zeros make numbers equal
    Don't assume 0.2 equals 0.22 because they look similar = wrong comparison! The digits in each place value position must match exactly. Always align decimal places and compare each position systematically.

Practice Quiz

Test your knowledge with interactive questions

Which decimal number is greater?

FAQ

Everything you need to know about this question

Why does 0.2 equal 0.20 but not 0.22?

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Adding trailing zeros after the last significant digit doesn't change the value - it's like saying 2 dollars and 20 dimes are the same! But 0.22 has 2 hundredths while 0.20 has 0 hundredths.

How do I know when decimals are really equal?

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Line up the decimal points and add zeros to make them the same length. Then compare digit by digit from left to right. If any digit differs, the numbers aren't equal!

What's the difference between 0.2 and 0.22?

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The difference is 0.22−0.20=0.02 0.22 - 0.20 = 0.02 or 2 hundredths. Think of it as 22 cents vs 20 cents - clearly different amounts!

Can I just ignore the zeros at the end?

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You can ignore trailing zeros when determining value, but not when comparing specific decimal representations. 0.2=0.20 0.2 = 0.20 but 0.2≠0.22 0.2 ≠ 0.22 .

Why is this important in real life?

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Precision matters! In money, measurements, and science, small differences like 0.02 can be significant. Always check your decimal places carefully.

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