Compare Decimals: Is 0.75 Equal to 0.750?

Decimal Equivalence with Trailing Zeros

Are the fractions equal?

0.75=?0.750 0.75 \stackrel{?}{=} 0.750

❤️ 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?

0.75=?0.750 0.75 \stackrel{?}{=} 0.750

2

Step-by-step solution

The question asks if the two decimal numbers 0.75 0.75 and 0.750 0.750 are equal. Decimal numbers can have trailing zeros which do not affect their value. Therefore, 0.75 0.75 is indeed equal to 0.750 0.750 because trailing zeros after the decimal point do not change the number's value. Hence, the fractions are equal.

3

Final Answer

= =

Key Points to Remember

Essential concepts to master this topic
  • Rule: Trailing zeros after decimal points don't change value
  • Technique: Compare 0.75=75100 0.75 = \frac{75}{100} and 0.750=7501000=75100 0.750 = \frac{750}{1000} = \frac{75}{100}
  • Check: Convert both to fractions with same denominator: both equal 34 \frac{3}{4}

Common Mistakes

Avoid these frequent errors
  • Thinking more digits means different value
    Don't assume 0.750 is different from 0.75 because it has more digits = wrong comparison! Extra zeros don't add value, they're just placeholders. Always remember that trailing zeros after the decimal point are meaningless for value.

Practice Quiz

Test your knowledge with interactive questions

Which decimal number is greater?

FAQ

Everything you need to know about this question

Why doesn't 0.750 have a different value than 0.75?

+

Think of it like money: 75 cents is 75 cents whether you write it as 0.75or0.75 or 0.750. The extra zero doesn't add any value - it's just an extra placeholder!

When do zeros actually matter in decimals?

+

Zeros matter when they're between the decimal point and other digits, like in 0.075. But trailing zeros at the end (like 0.750) don't change the value at all.

How can I check if two decimals are equal?

+

Convert both to fractions and simplify, or line up the decimal points and compare digit by digit. You can also subtract them - if you get zero, they're equal!

Is 0.5 the same as 0.50 and 0.500?

+

Yes! All three represent exactly 12 \frac{1}{2} . You can add as many trailing zeros as you want without changing the decimal's value.

What about 0.70 versus 0.07?

+

These are completely different! 0.70 equals 710 \frac{7}{10} while 0.07 equals 7100 \frac{7}{100} . The zero's position matters, but trailing zeros don't.

🌟 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