Master the Sign: Comparing 3/5 to 0.65

Q: Why can't I just compare 3 to 0.65 directly?

Because $ \frac{3}{5} $ means 3 divided by 5, not just 3! You must perform the division to get the true value of 0.6 before comparing.

Q: What if the fraction doesn't divide evenly?

That's okay! For example, $ \frac{1}{3} = 0.333... $ Keep enough decimal places to make an accurate comparison, usually 2-3 places is sufficient.

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

Absolutely! Convert 0.65 to $ \frac{65}{100} = \frac{13}{20} $, then compare $ \frac{3}{5} $ and $ \frac{13}{20} $ using common denominators.

Q: How do I compare 0.6 and 0.65 easily?

Think of them as 0.60 and 0.65. Now you can see that 60 hundredths is less than 65 hundredths, so 0.6

Q: What if I get confused about which direction the symbol points?

Remember: the symbol always points to the smaller number. Since 0.6 is smaller, \( \frac{3}{5} with the point facing left toward the smaller value.

Fraction-Decimal Comparisons with Mixed Forms

Choose the appropriate sign:

$\frac{3}{5}?0.65$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Choose the appropriate sign:

$\frac{3}{5}?0.65$

Step-by-step solution

To solve this problem, we need to compare the fraction $\frac{3}{5}$ with the decimal $0.65$ . We'll begin by converting the fraction into a decimal form.

Step 1: Convert the fraction $\frac{3}{5}$ to a decimal.

This is done by dividing the numerator by the denominator: $\frac{3}{5} = 3 \div 5 = 0.6$ .

Step 2: Compare the results.

We now have $0.6$ from $\frac{3}{5}$ and $0.65$ provided in the problem.

Step 3: Analyze the numbers.

Comparing $0.6$ and $0.65$ , we can see that $0.6$ is less than $0.65$ .

Thus, the fraction $\frac{3}{5}$ is less than the decimal $0.65$ .

Therefore, the appropriate sign to complete $\frac{3}{5} ? 0.65$ is $<$ .

The solution is: $\frac{3}{5} < 0.65$ .

Final Answer

$<$

Key Points to Remember

Essential concepts to master this topic

Conversion Rule: Change fraction to decimal by dividing numerator by denominator
Technique: $\frac{3}{5} = 3 \div 5 = 0.6$ for direct comparison
Check: Compare decimal places: 0.6 vs 0.65 shows 0.6 < 0.65 ✓

Common Mistakes

Avoid these frequent errors

Comparing numerator directly to decimal
Don't compare 3 to 0.65 thinking 3 > 0.65 = wrong answer! This ignores the denominator completely and leads to incorrect comparisons. Always convert the fraction to decimal form first by dividing 3 ÷ 5 = 0.6, then compare 0.6 to 0.65.

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 3 to 0.65 directly?

Because $\frac{3}{5}$ means 3 divided by 5, not just 3! You must perform the division to get the true value of 0.6 before comparing.

What if the fraction doesn't divide evenly?

That's okay! For example, $\frac{1}{3} = 0.333...$ Keep enough decimal places to make an accurate comparison, usually 2-3 places is sufficient.

Can I convert the decimal to a fraction instead?

Absolutely! Convert 0.65 to $\frac{65}{100} = \frac{13}{20}$ , then compare $\frac{3}{5}$ and $\frac{13}{20}$ using common denominators.

How do I compare 0.6 and 0.65 easily?

Think of them as 0.60 and 0.65. Now you can see that 60 hundredths is less than 65 hundredths, so 0.6 < 0.65.

What if I get confused about which direction the symbol points?

Remember: the symbol always points to the smaller number. Since 0.6 is smaller, $\frac{3}{5} < 0.65$ with the point facing left toward the smaller value.

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