Compare Decimals: Is 0.25 Equal to 0.250?

Decimal Equivalence with Trailing Zeros

Are they the same numbers?

0.25=?0.250 0.25\stackrel{?}{=}0.250

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:07 Are the numbers exactly the same?
00:10 Remember, you can always add a zero to the rightmost digit. This keeps the number the same.
00:18 It looks like these numbers are equal.
00:21 And that's how we find our solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Are they the same numbers?

0.25=?0.250 0.25\stackrel{?}{=}0.250

2

Step-by-step solution

We will add 0 to the number 0.25 in the following way:

0.25=0.250 0.25=0.250

And we will discover that the numbers are identical

3

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic
  • Rule: Trailing zeros after decimal point do not change value
  • Technique: Compare 0.25 and 0.250 by adding zeros: 0.250 = 0.250
  • Check: Convert to fractions: 25/100 = 250/1000 = 1/4 ✓

Common Mistakes

Avoid these frequent errors
  • Thinking more digits means larger number
    Don't assume 0.250 is bigger than 0.25 because it has more digits = wrong comparison! Extra zeros after the decimal don't add value, they're just placeholders. Always focus on the actual digit values and their positions.

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 doesn't 0.250 equal a bigger number than 0.25?

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The trailing zero in 0.250 is just a placeholder! It's like writing $5.00 instead of $5 - the value stays exactly the same. The zero in the thousandths place doesn't add any value.

When do zeros actually change a decimal's value?

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Zeros change the value when they're between the decimal point and other digits. For example: 0.025 ≠ 0.25 because the zero holds the tenths place, making 0.025 much smaller.

How can I prove these decimals are equal?

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Try these methods:

  • Convert to fractions: 25100=2501000 \frac{25}{100} = \frac{250}{1000}
  • Line up decimal places: 0.250 vs 0.250
  • Use a number line - they're the same point!

Is it better to write 0.25 or 0.250?

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Both are mathematically correct! However, 0.25 is simpler and more common. Write 0.250 only when you need to show precision to the thousandths place for specific contexts.

What about 0.2500 or 0.25000?

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All of these equal the same value: 0.25 = 0.250 = 0.2500 = 0.25000. You can add as many trailing zeros as you want without changing the decimal's value!

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