Decimal Comparison: Determining if 0.500 = 0.5 Using Number Line

Q: Why does 0.500 equal 0.5 if they look different?

They represent the exact same value! The zeros after 5 are called trailing zeros and don't change the number's value, just like how 007 equals 7.

Q: Does this work for all decimals with extra zeros?

Yes! $ 0.30 = 0.3 $, $ 2.100 = 2.1 $, and $ 0.7000 = 0.7 $. Trailing zeros never change a decimal's value.

Q: What about zeros in the middle of a decimal?

Those are different! In 0.105, the zero is significant because removing it would make 0.15, which is a different number entirely.

Q: How do I use a number line to check this?

Both 0.500 and 0.5 will be at the exact same point on the number line - halfway between 0 and 1. Same position means same value!

Decimal Equivalence with Trailing Zeros

Determine the appropriate sign according to the number line:

$0.500?\text{0}.5$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:07 First, let's choose the correct sign for our problem.

00:11 Next, we'll use a number line to locate our two numbers.

00:15 Remember, in a decimal, the last digit comes after the decimal point.

00:20 We can add as many zeros as we like, and the value stays the same.

00:25 So, the numbers are equal. And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Determine the appropriate sign according to the number line:

$0.500?\text{0}.5$

Step-by-step solution

Let's look at the number 0.500

Since the zeros after the tenths digit are not relevant, we can argue that:

$0.500=0.5$

Therefore, if we compare the two numbers, we will find that they are equal and it's the same number:

$0.5=0.5$

Final Answer

$=$

Key Points to Remember

Essential concepts to master this topic

Rule: Trailing zeros after decimal point don't change value
Technique: Remove extra zeros: 0.500 becomes 0.5 (same value)
Check: Both numbers occupy same position on number line ✓

Common Mistakes

Avoid these frequent errors

Thinking more digits means different value
Don't assume 0.500 is different from 0.5 because it has more digits = wrong comparison! Extra zeros are just placeholders that don't change the actual value. Always focus on the significant digits and ignore trailing zeros.

Practice Quiz

Test your knowledge with interactive questions

Which decimal number is greater?

FAQ

Everything you need to know about this question

Why does 0.500 equal 0.5 if they look different?

They represent the exact same value! The zeros after 5 are called trailing zeros and don't change the number's value, just like how 007 equals 7.

How can I tell if two decimals are equal?

Remove all trailing zeros from both numbers, then compare. If they look identical after removing zeros, they're equal!

Does this work for all decimals with extra zeros?

Yes! $0.30 = 0.3$ , $2.100 = 2.1$ , and $0.7000 = 0.7$ . Trailing zeros never change a decimal's value.

What about zeros in the middle of a decimal?

Those are different! In 0.105, the zero is significant because removing it would make 0.15, which is a different number entirely.

How do I use a number line to check this?

Both 0.500 and 0.5 will be at the exact same point on the number line - halfway between 0 and 1. Same position means same value!

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