Compare Fractions and Decimals: Is 4/5 >, <, or = to 0.8?

Q: How do I know when a fraction equals a decimal?

Convert both to the same format! Either change the decimal to a fraction (like 0.8 = $ \frac{8}{10} $) or divide the fraction (like $ \frac{4}{5} = 4 ÷ 5 = 0.8 $).

Q: Why do we simplify fractions when comparing?

Simplifying helps you see if fractions are equal! When $ \frac{8}{10} $ becomes $ \frac{4}{5} $, it's easier to recognize they're the same value in different forms.

Q: Can I just convert the fraction to a decimal instead?

Absolutely! Dividing $ \frac{4}{5} = 4 ÷ 5 = 0.8 $ is another perfect way. Use whichever method feels more comfortable to you.

Q: What if the decimal has more than one digit after the decimal point?

Same process! For 0.75, write it as $ \frac{75}{100} $, then simplify to $ \frac{3}{4} $. The number of decimal places tells you the denominator (10, 100, 1000, etc.).

Q: How can I check my comparison is correct?

Convert both numbers to the same form and verify they match! Also, you can use a calculator: $ \frac{4}{5} = 0.8 $ exactly.

Decimal-Fraction Equivalence with Mixed Representations

Choose the appropriate sign (?):

$\frac{4}{5}?0.8$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 First, choose the correct sign. Take your time to think it through.

00:14 Next, let's convert the decimal number into a fraction. We'll do this step by step.

00:23 Now, simplify the fraction as much as possible. This is an important step!

00:29 Remember, divide both the top number and the bottom number. You can do it!

00:34 Look closely. You'll see that the numbers are equal. Great job!

00:39 And that's how we find the solution to the problem. Well done!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Choose the appropriate sign (?):

$\frac{4}{5}?0.8$

Step-by-step solution

First, let's convert 0.8 into a simple fraction.

Since there is only one number after the decimal point, we can divide by 10 as follows:

$0.8=\frac{8}{10}$

Let's simplify the fraction so that we have two fractions with the same denominator:

$\frac{8:2}{10:2}=\frac{4}{5}$

Now we can compare and see that:

$\frac{4}{5}=\frac{4}{5}$

Final Answer

$=$

Key Points to Remember

Essential concepts to master this topic

Conversion Rule: Convert decimal to fraction to compare equivalent values
Technique: Transform 0.8 to $\frac{8}{10}$ then simplify to $\frac{4}{5}$
Check: Both forms equal 0.8, so $\frac{4}{5} = 0.8$ confirms equality ✓

Common Mistakes

Avoid these frequent errors

Assuming fractions and decimals with different appearances are unequal
Don't think $\frac{4}{5}$ is different from 0.8 just because they look different = wrong comparison! These are just different ways to write the same value. Always convert to matching forms before comparing.

Practice Quiz

Test your knowledge with interactive questions

Are they the same numbers?

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

FAQ

Everything you need to know about this question

How do I know when a fraction equals a decimal?

Convert both to the same format! Either change the decimal to a fraction (like 0.8 = $\frac{8}{10}$ ) or divide the fraction (like $\frac{4}{5} = 4 ÷ 5 = 0.8$ ).

Why do we simplify fractions when comparing?

Simplifying helps you see if fractions are equal! When $\frac{8}{10}$ becomes $\frac{4}{5}$ , it's easier to recognize they're the same value in different forms.

Can I just convert the fraction to a decimal instead?

Absolutely! Dividing $\frac{4}{5} = 4 ÷ 5 = 0.8$ is another perfect way. Use whichever method feels more comfortable to you.

What if the decimal has more than one digit after the decimal point?

Same process! For 0.75, write it as $\frac{75}{100}$ , then simplify to $\frac{3}{4}$ . The number of decimal places tells you the denominator (10, 100, 1000, etc.).

How can I check my comparison is correct?

Convert both numbers to the same form and verify they match! Also, you can use a calculator: $\frac{4}{5} = 0.8$ exactly.

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