Decimal Comparison: Is 0.707 Equal to 0.7007?

Decimal Comparison with Place Value Analysis

Are the fractions equal?

0.707=?0.7007 0.707 \stackrel{?}{=} 0.7007

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Are the fractions equal?

0.707=?0.7007 0.707 \stackrel{?}{=} 0.7007

2

Step-by-step solution

To determine if the fractions are equal, examine each digit of the decimal numbers.

In the number 0.707 0.707 , the digits are 0, 7, and 7.

In the number 0.7007 0.7007 , the digits are 0, 7, 0, and 7.

The first fraction, 0.707 0.707 , has no digit in the thousandths place, but the second fraction, 0.7007 0.7007 , contains a zero in the thousandths place.

Thus, 0.7070.7007 0.707 \neq 0.7007 .

3

Final Answer

\neq

Key Points to Remember

Essential concepts to master this topic
  • Place Value: Each decimal position represents a different power of ten
  • Technique: Compare digits from left to right: 0.707 vs 0.7007
  • Check: Convert to same decimal places: 0.7070 ≠ 0.7007 ✓

Common Mistakes

Avoid these frequent errors
  • Assuming shorter decimals equal longer ones
    Don't think 0.707 = 0.7007 just because they look similar! The extra zero in the thousandths place changes the value. Always compare each decimal place carefully or add trailing zeros to match lengths.

Practice Quiz

Test your knowledge with interactive questions

Which decimal number is greater?

FAQ

Everything you need to know about this question

Why can't I just ignore the extra zero in 0.7007?

+

That zero is in the thousandths place, which makes the number smaller! Think of it as 7007/10000 vs 707/1000. The zero matters because it affects the actual value.

How do I compare decimals with different numbers of digits?

+

Add trailing zeros to make them the same length: 0.707 becomes 0.7070. Now compare: 0.7070 vs 0.7007. You can clearly see they're different!

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

+

Line them up by decimal point and compare digit by digit from left to right. The first place where digits differ tells you they're not equal.

Can I convert these to fractions to compare?

+

Absolutely! 0.707=7071000 0.707 = \frac{707}{1000} and 0.7007=700710000 0.7007 = \frac{7007}{10000} . Since the numerators and denominators are different, the fractions aren't equal.

Does adding zeros at the end change a decimal's value?

+

No! Adding zeros to the right doesn't change value: 0.5 = 0.50 = 0.500. But zeros in the middle (like between 7s) do change the value!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Decimal Fractions - Basic questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations