Compare Fractions and Decimals: Determine if 1/5 is Greater Than, Less Than, or Equal to 0.5

Q: Why can't I just compare the numbers 1, 5, and 0.5 directly?

Because fractions and decimals use different formats! The fraction $ \frac{1}{5} $ means "1 divided by 5," which equals 0.2. You must convert to the same format before comparing.

Q: Is there another way to solve this besides converting to decimals?

Yes! You could convert 0.5 to a fraction: $ 0.5 = \frac{5}{10} = \frac{1}{2} $. Then compare $ \frac{1}{5} $ and $ \frac{1}{2} $ using cross multiplication or common denominators.

Q: How do I remember which decimal is bigger when comparing 0.2 and 0.5?

Think about place values! Both have the same tenths place, but 0.5 has 5 tenths while 0.2 has only 2 tenths. Since 5 > 2, we know 0.5 > 0.2.

Q: Can I use a calculator for the division?

Absolutely! Calculators are great for converting fractions to decimals. Just remember to understand the process - you're dividing the top number by the bottom number.

Fraction-Decimal Comparison with Division Conversion

Choose the appropriate sign (?):

$\frac{1}{5}?0.5$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 First, choose the right sign for this problem.

00:08 Next, expand the fraction until the denominator is ten.

00:13 Make sure to multiply both the top and the bottom numbers by the same amount. This keeps the fraction equal.

00:22 Now, let's switch from a fraction to a decimal fraction format.

00:26 Write down the whole number from the top of the fraction.

00:31 Because the bottom number is ten, move the decimal point one place to the left.

00:36 Replace the fraction with this new decimal and compare them.

00:40 Choose the correct sign to compare.

00:44 And there you have it! That's how we solve this question.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Choose the appropriate sign (?):

$\frac{1}{5}?0.5$

Step-by-step solution

To solve this problem, we'll first convert the fraction $\frac{1}{5}$ to a decimal to directly compare it with $0.5$ .

Step 1: Convert $\frac{1}{5}$ to a decimal.
Step 2: Compare the results.

Let's work through these steps:
Step 1: Conversion of $\frac{1}{5}$ . This can be done by performing the division $1 \div 5 = 0.2$ .
Now, we have two decimals to compare: $0.2$ and $0.5$ .

Step 2: Compare $0.2$ and $0.5$ .
Since $0.2$ is less than $0.5$ , $\frac{1}{5}$ is less than $0.5$ .

Therefore, the correct sign to use is $"<"$ .

The inequality can be represented as $\frac{1}{5} < 0.5$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Conversion Rule: Divide numerator by denominator to get decimal form
Division Method: Calculate 1 ÷ 5 = 0.2 for comparison
Verification: Check that 0.2 < 0.5 makes sense visually ✓

Common Mistakes

Avoid these frequent errors

Comparing fractions and decimals without converting
Don't try to compare $\frac{1}{5}$ directly with 0.5 = confusion and wrong answers! You can't easily tell which is bigger without converting. Always convert the fraction to decimal form first by dividing: 1 ÷ 5 = 0.2.

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 the numbers 1, 5, and 0.5 directly?

Because fractions and decimals use different formats! The fraction $\frac{1}{5}$ means "1 divided by 5," which equals 0.2. You must convert to the same format before comparing.

Is there another way to solve this besides converting to decimals?

Yes! You could convert 0.5 to a fraction: $0.5 = \frac{5}{10} = \frac{1}{2}$ . Then compare $\frac{1}{5}$ and $\frac{1}{2}$ using cross multiplication or common denominators.

How do I remember which decimal is bigger when comparing 0.2 and 0.5?

Think about place values! Both have the same tenths place, but 0.5 has 5 tenths while 0.2 has only 2 tenths. Since 5 > 2, we know 0.5 > 0.2.

What if I get a long decimal when dividing fractions?

That's normal! Just calculate enough decimal places to make the comparison clear. For example, $\frac{1}{3} = 0.333...$ and you only need a few decimal places to compare with other numbers.

Can I use a calculator for the division?

Absolutely! Calculators are great for converting fractions to decimals. Just remember to understand the process - you're dividing the top number by the bottom number.

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