Compare Fraction and Decimal: 1/5 ? 0.22 - Select the Correct Sign

Q: Why can't I just compare 1/5 and 0.22 directly?

Different number forms make comparison tricky! It's like comparing apples and oranges. Converting both to the same form (decimals or fractions) makes the comparison clear and accurate.

Q: Is there a faster way to convert 1/5 to a decimal?

Yes! Since 5 × 2 = 10, multiply both numerator and denominator by 2: $ \frac{1}{5} × \frac{2}{2} = \frac{2}{10} = 0.2 $. You can also just divide: 1 ÷ 5 = 0.2.

Q: What if I get different decimal places when comparing?

Add zeros to make them the same length! For example, 0.2 becomes 0.20 when comparing to 0.22. This makes it easier to see which is larger.

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

Absolutely! Convert 0.22 to $ \frac{22}{100} $, then compare $ \frac{1}{5} = \frac{20}{100} $ with $ \frac{22}{100} $. Since 20 \( \frac{1}{5} .

Q: How do I remember which conversion method to use?

Choose the method that gives you easier numbers to work with. Converting to decimals is often simpler, but if you're more comfortable with fractions, that works too!

Fraction-Decimal Comparison with Conversion Methods

Choose the appropriate sign:

$\frac{1}{5}?0.22$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Choose the appropriate sign

00:04 Multiply the fraction by 2 to find the common denominator

00:21 Convert from fraction to decimal number

00:35 Compare the digits to find the larger number

00:41 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Choose the appropriate sign:

$\frac{1}{5}?0.22$

Step-by-step solution

First, let's convert the simple fraction into a decimal fraction.

We'll multiply the fraction so that we get 10 in the denominator:

$\frac{1}{5}\times\frac{2}{2}=\frac{2}{10}$

Now let's convert the simple fraction we got to a decimal fraction.

Let's write the number 2 as a decimal fraction:

$2=2.$

Since the simple fraction we got is divisible by 10, we'll move the decimal point one place to the left and get:

$2.=.2=0.2$

Let's compare the two decimal numbers we got. We'll add 0 to the number 0.2:

$0.20 < 0.22$

Final Answer

$<$

Key Points to Remember

Essential concepts to master this topic

Rule: Convert fractions to decimals to compare directly
Technique: $\frac{1}{5} = \frac{2}{10} = 0.2$ by multiplying by equivalent fraction
Check: Compare place values: 0.20 vs 0.22 shows 20 < 22 hundredths ✓

Common Mistakes

Avoid these frequent errors

Comparing fraction and decimal without converting
Don't try to compare $\frac{1}{5}$ and 0.22 directly = confusion and wrong answers! You can't properly compare different number forms. Always convert both to the same form (both decimals or both fractions) first.

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 compare 1/5 and 0.22 directly?

Different number forms make comparison tricky! It's like comparing apples and oranges. Converting both to the same form (decimals or fractions) makes the comparison clear and accurate.

Is there a faster way to convert 1/5 to a decimal?

Yes! Since 5 × 2 = 10, multiply both numerator and denominator by 2: $\frac{1}{5} × \frac{2}{2} = \frac{2}{10} = 0.2$ . You can also just divide: 1 ÷ 5 = 0.2.

What if I get different decimal places when comparing?

Add zeros to make them the same length! For example, 0.2 becomes 0.20 when comparing to 0.22. This makes it easier to see which is larger.

Can I convert the decimal to a fraction instead?

Absolutely! Convert 0.22 to $\frac{22}{100}$ , then compare $\frac{1}{5} = \frac{20}{100}$ with $\frac{22}{100}$ . Since 20 < 22, we have $\frac{1}{5} < 0.22$ .

How do I remember which conversion method to use?

Choose the method that gives you easier numbers to work with. Converting to decimals is often simpler, but if you're more comfortable with fractions, that works too!

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