Decimal Comparison: Is 0.1 Equal to 0.10?

Q: Why does 0.1 equal 0.10 if they look different?

They look different but represent the same amount! Think of it like saying 'one dollar' vs 'one dollar and zero cents' - both mean exactly the same thing.

Q: Can I add as many zeros as I want after the decimal?

Yes! You can write 0.1 as 0.10, 0.100, or 0.1000 - they're all equal. The zeros after the last non-zero digit are called trailing zeros and don't change the value.

Q: Is this the same for whole numbers too?

No! For whole numbers, adding zeros changes the value (10 ≠ 100). But for decimals, zeros after the last significant digit don't change the value.

Q: What's the easiest way to check if two decimals are equal?

Convert both to fractions! $ 0.1 = \frac{1}{10} $ and $ 0.10 = \frac{10}{100} = \frac{1}{10} $. Same fraction means equal decimals!

Decimal Equivalence with Trailing Zeros

Are they the same numbers?

$0.1\stackrel{?}{=}0.10$

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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?

00:11 We can always add zero after the last digit. This doesn't change the value.

00:16 So, the numbers are indeed the same.

00:20 And that's how we solve the problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Are they the same numbers?

$0.1\stackrel{?}{=}0.10$

Step-by-step solution

We will add 0 to the number 0.1 in the following way:

$0.1=0.10$

And we will discover that the numbers are indeed identical

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic

Rule: Adding zeros after decimal point doesn't change value
Technique: Compare place values: 0.1 = 1 tenth = 0.10
Check: Convert to fractions: 1/10 = 10/100 = same value ✓

Common Mistakes

Avoid these frequent errors

Thinking more digits means different value
Don't assume 0.10 is different from 0.1 because it has more digits = wrong comparison! Extra zeros after the last significant digit don't change the decimal's value. Always focus on the actual digit values and their place positions.

Practice Quiz

Test your knowledge with interactive questions

Which decimal number is greater?

FAQ

Everything you need to know about this question

Why does 0.1 equal 0.10 if they look different?

They look different but represent the same amount! Think of it like saying 'one dollar' vs 'one dollar and zero cents' - both mean exactly the same thing.

Can I add as many zeros as I want after the decimal?

Yes! You can write 0.1 as 0.10, 0.100, or 0.1000 - they're all equal. The zeros after the last non-zero digit are called trailing zeros and don't change the value.

How do I know which decimal is bigger when comparing?

Compare digits from left to right after the decimal point. If one number has trailing zeros, ignore them and compare the actual digit values in each place.

Is this the same for whole numbers too?

No! For whole numbers, adding zeros changes the value (10 ≠ 100). But for decimals, zeros after the last significant digit don't change the value.

What's the easiest way to check if two decimals are equal?

Convert both to fractions! $0.1 = \frac{1}{10}$ and $0.10 = \frac{10}{100} = \frac{1}{10}$ . Same fraction means equal decimals!

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