Compare Fractions and Decimals: Determining the Relationship Between 1/4 and 0.4

Q: Why can't I just compare 1/4 and 0.4 without converting?

You need numbers in the same format to compare accurately! It's like trying to compare apples and oranges - you need a common way to measure them first.

Q: Should I convert the decimal to a fraction instead?

Either method works! You could convert 0.4 to $ \frac{4}{10} = \frac{2}{5} $, then compare $ \frac{1}{4} $ and $ \frac{2}{5} $. But converting fractions to decimals is usually easier.

Q: How do I remember that 1/4 equals 0.25?

Think of quarters! A quarter (1/4) of a dollar is 25 cents, so $ \frac{1}{4} = 0.25 $. This real-world connection helps you remember!

Q: What if I get a long decimal when converting?

Some fractions create repeating decimals like $ \frac{1}{3} = 0.333... $. Just use enough decimal places to make an accurate comparison - usually 2-3 places is enough.

Q: Is there a faster way to compare without full conversion?

Yes! You can use cross-multiplication for fractions vs decimals. Compare $ \frac{1}{4} $ and 0.4 by checking if 1 × 10

Fraction-Decimal Comparison with Converting Methods

Choose the appropriate sign (?):

$\frac{1}{4}?0.4$

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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.

00:10 Next, expand the fraction so the bottom number is one hundred.

00:15 Remember to multiply both the top and bottom numbers.

00:25 Now, let's change the fraction into a decimal.

00:29 Write the top number as a full number.

00:33 Since the bottom number is one hundred, move the decimal point two spaces left.

00:41 Replace the fraction with the decimal.

00:50 And that's how we solve the problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Choose the appropriate sign (?):

$\frac{1}{4}?0.4$

Step-by-step solution

To compare $\frac{1}{4}$ and $0.4$ , we first convert $\frac{1}{4}$ to a decimal:

Step 1: Convert $\frac{1}{4}$ to a decimal.

$\frac{1}{4}$ is the same as dividing 1 by 4. Performing this division, we get:

$\frac{1}{4} = 0.25$

Step 2: Compare the decimals.

Now, we compare $0.25$ with $0.4$ :

$0.25 < 0.4$

Therefore, the appropriate sign to use is <.

The comparison between $\frac{1}{4}$ and $0.4$ is $\frac{1}{4} < 0.4$ .

Therefore, the correct choice is: $<$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Conversion Rule: Convert fractions to decimals by dividing numerator by denominator
Technique: $\frac{1}{4} = 1 \div 4 = 0.25$ for direct comparison
Check: Compare decimal places: 0.25 has 5 < 4 in tenths place ✓

Common Mistakes

Avoid these frequent errors

Comparing fractions and decimals without converting
Don't try to compare $\frac{1}{4}$ and 0.4 directly without converting = wrong comparison! You can't properly compare different number formats. Always convert to the same format first (both decimals or both fractions).

Practice Quiz

Test your knowledge with interactive questions

Convert into fraction form:

$$ 0.38= $$

FAQ

Everything you need to know about this question

Why can't I just compare 1/4 and 0.4 without converting?

You need numbers in the same format to compare accurately! It's like trying to compare apples and oranges - you need a common way to measure them first.

Should I convert the decimal to a fraction instead?

Either method works! You could convert 0.4 to $\frac{4}{10} = \frac{2}{5}$ , then compare $\frac{1}{4}$ and $\frac{2}{5}$ . But converting fractions to decimals is usually easier.

How do I remember that 1/4 equals 0.25?

Think of quarters! A quarter (1/4) of a dollar is 25 cents, so $\frac{1}{4} = 0.25$ . This real-world connection helps you remember!

What if I get a long decimal when converting?

Some fractions create repeating decimals like $\frac{1}{3} = 0.333...$ . Just use enough decimal places to make an accurate comparison - usually 2-3 places is enough.

Is there a faster way to compare without full conversion?

Yes! You can use cross-multiplication for fractions vs decimals. Compare $\frac{1}{4}$ and 0.4 by checking if 1 × 10 < 4 × 4, which gives 10 < 16 ✓

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