Decimal Comparison: Is 0.02 Equal to 0.002?

Q: Why does 0.02 not equal 0.002 if they both have a 2?

The position of the 2 matters! In $ 0.02 $, the 2 is in the hundredths place, but in $ 0.002 $, it's in the thousandths place. Different positions mean different values.

Q: How can I remember which decimal is bigger?

Add trailing zeros to make them the same length: $ 0.020 $ vs $ 0.002 $. Now compare digit by digit from left to right: 20 thousandths is bigger than 2 thousandths!

Q: What's the difference between 0.02 and 0.002?

$ 0.02 = \frac{2}{100} $ (2 hundredths) while $ 0.002 = \frac{2}{1000} $ (2 thousandths). The first is 10 times larger than the second!

Q: Do trailing zeros ever change a number's value?

Trailing zeros after the decimal point don't change value, but they help with comparison! $ 0.02 = 0.020 = 0.0200 $ - all the same number.

Decimal Place Value with Trailing Zeros

Are they the same numbers?

$0.02\stackrel{?}{=}0.002$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:07 Are the numbers the same? Let's find out.

00:17 First, let's compare each digit in both numbers.

00:22 We see that 2 is greater than 0. So, this number is bigger, meaning they aren't the same.

00:28 And that's how we solve the question!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Are they the same numbers?

$0.02\stackrel{?}{=}0.002$

Step-by-step solution

We will add 0 to the number 0.02 in the following way:

$0.02=0.020$

And we will discover that the numbers are not identical

Final Answer

Key Points to Remember

Essential concepts to master this topic

Place Value: Each decimal position has a different value (tenths vs hundredths)
Technique: Add trailing zeros to compare: 0.02 = 0.020 vs 0.002
Check: Read aloud: two hundredths vs two thousandths are different ✓

Common Mistakes

Avoid these frequent errors

Thinking trailing zeros don't matter
Don't ignore decimal place positions when comparing = wrong conclusions! Each position (tenths, hundredths, thousandths) represents different values. Always count decimal places carefully to determine the true value.

Practice Quiz

Test your knowledge with interactive questions

Which decimal number is greater?

FAQ

Everything you need to know about this question

Why does 0.02 not equal 0.002 if they both have a 2?

The position of the 2 matters! In $0.02$ , the 2 is in the hundredths place, but in $0.002$ , it's in the thousandths place. Different positions mean different values.

How can I remember which decimal is bigger?

Add trailing zeros to make them the same length: $0.020$ vs $0.002$ . Now compare digit by digit from left to right: 20 thousandths is bigger than 2 thousandths!

What's the difference between 0.02 and 0.002?

$0.02 = \frac{2}{100}$ (2 hundredths) while $0.002 = \frac{2}{1000}$ (2 thousandths). The first is 10 times larger than the second!

Do trailing zeros ever change a number's value?

Trailing zeros after the decimal point don't change value, but they help with comparison! $0.02 = 0.020 = 0.0200$ - all the same number.

How do I read decimal numbers correctly?

Read the whole number, say "and" for the decimal point, then read the decimal part with its place value. $0.02$ is "zero and two hundredths".

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