Compare Fraction and Decimal: 3/50 vs 0.06

Q: Why do I need to convert the fraction to a decimal?

Converting to the same form makes comparison much easier! It's hard to compare $ \frac{3}{50} $ and 0.06 directly, but once you see both as 0.06, the answer is obvious.

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

Absolutely! You could write 0.06 as $ \frac{6}{100} = \frac{3}{50} $. Either way works - just pick the conversion that feels easier to you.

Q: How do I divide 3 by 50 without a calculator?

Think of it as $ \frac{3}{50} = \frac{6}{100} $. Since per hundred means percent, $ \frac{6}{100} = 0.06 $. You can also do long division: 3.00 ÷ 50.

Q: What if the decimal has more digits than the fraction?

Sometimes decimals are longer when converted! For example, $ \frac{1}{3} = 0.333... $ But you can still compare by rounding to the same number of decimal places or keeping the exact fraction form.

Q: Are there any shortcuts for common fractions?

Yes! Learn these common ones: $ \frac{1}{2} = 0.5 $, $ \frac{1}{4} = 0.25 $, $ \frac{1}{5} = 0.2 $, $ \frac{1}{10} = 0.1 $. These will help you convert faster!

Fraction Comparison with Decimal Conversion

Choose the appropriate sign (?):

$\frac{3}{50}?0.06$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Choose the appropriate sign

00:03 Expand the fraction so the denominator equals 100

00:09 Make sure to multiply both numerator and denominator

00:19 Now let's convert from fraction to decimal

00:22 Write the numerator as a whole number

00:26 When denominator equals 100, move the decimal point 2 places left

00:34 Place the decimal instead of the fraction, and compare

00:38 Choose the correct sign

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 (?):

$\frac{3}{50}?0.06$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Convert the fraction $\frac{3}{50}$ to a decimal.
Step 2: Compare the decimal value of $\frac{3}{50}$ to $0.06$ .
Step 3: Determine the correct comparison sign.

Now, let's work through each step:

Step 1: Convert $\frac{3}{50}$ to a decimal. This is done by dividing 3 by 50:

$\frac{3}{50} = 0.06$

Step 2: Compare the decimal value $0.06$ to $0.06$ .

Since both decimal values are the same, the two expressions are equal.

Step 3: Therefore, the comparison sign that satisfies the condition is $=$ .

Thus, the correct answer to the problem is =.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Conversion Rule: Divide numerator by denominator to get decimal form
Technique: Calculate $\frac{3}{50} = 3 \div 50 = 0.06$
Check: Convert both to same form then compare: 0.06 = 0.06 ✓

Common Mistakes

Avoid these frequent errors

Comparing fraction and decimal without converting
Don't try to compare $\frac{3}{50}$ and 0.06 directly without converting = impossible to see they're equal! Mixed forms make comparison confusing and lead to wrong answers. Always convert both numbers to the same form first.

Practice Quiz

Test your knowledge with interactive questions

Write the following fraction as a decimal:

$\frac{5}{100}=$

FAQ

Everything you need to know about this question

Why do I need to convert the fraction to a decimal?

Converting to the same form makes comparison much easier! It's hard to compare $\frac{3}{50}$ and 0.06 directly, but once you see both as 0.06, the answer is obvious.

Can I convert the decimal to a fraction instead?

Absolutely! You could write 0.06 as $\frac{6}{100} = \frac{3}{50}$ . Either way works - just pick the conversion that feels easier to you.

How do I divide 3 by 50 without a calculator?

Think of it as $\frac{3}{50} = \frac{6}{100}$ . Since per hundred means percent, $\frac{6}{100} = 0.06$ . You can also do long division: 3.00 ÷ 50.

What if the decimal has more digits than the fraction?

Sometimes decimals are longer when converted! For example, $\frac{1}{3} = 0.333...$ But you can still compare by rounding to the same number of decimal places or keeping the exact fraction form.

Are there any shortcuts for common fractions?

Yes! Learn these common ones: $\frac{1}{2} = 0.5$ , $\frac{1}{4} = 0.25$ , $\frac{1}{5} = 0.2$ , $\frac{1}{10} = 0.1$ . These will help you convert faster!

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