Compare Fraction and Decimal: Is 2/3 Greater Than, Less Than, or Equal to 0.6?

Q: Should I convert the fraction to decimal or the decimal to fraction?

Either method works! Converting 0.6 to $ \frac{3}{5} $ often gives exact fractions that are easier to compare. Converting fractions to decimals works too, but might give long decimal approximations.

Q: How do I find the common denominator between 3 and 5?

Find the Least Common Multiple (LCM) of the denominators. For 3 and 5, list multiples: 3, 6, 9, 12, 15 and 5, 10, 15. The LCM is 15!

Q: Why can't I just cross-multiply to compare fractions?

Cross-multiplication works great! For $ \frac{2}{3} $ vs $ \frac{3}{5} $, compare 2×5 = 10 and 3×3 = 9. Since 10 > 9, we have $ \frac{2}{3} > \frac{3}{5} $.

Q: What if I get a messy decimal when converting fractions?

That's normal! $ \frac{2}{3} = 0.666... $ (repeating). You only need enough decimal places to see which is larger. Here, 0.667 > 0.6 is clear.

Q: Is there a faster way to compare these specific numbers?

Yes! Notice that 0.6 = 60% and $ \frac{2}{3} $ = 66.7%. Thinking in percentages can make comparisons quicker and more intuitive.

Fraction Comparison with Decimal Conversion

Choose the appropriate sign:

$\frac{2}{3}?0.6$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 First, select the right mathematical sign to use.

00:13 Next, change the decimal number into a fraction. It's easy!

00:23 Try to simplify the fraction as much as you can.

00:27 Remember to divide both the top number, the numerator, and the bottom number, the denominator.

00:42 Then, multiply the fraction by the second denominator to find a common denominator.

00:49 Be sure to multiply top by top and bottom by bottom. You got this!

00:55 Use this same method for the second fraction.

01:00 Alright! Now, let's compare the fractions to see which is larger or smaller.

01:06 And that's how we solve the problem. Well done!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Choose the appropriate sign:

$\frac{2}{3}?0.6$

Step-by-step solution

First, let's convert 0.6 to a simple fraction.

Since there is only one digit after the decimal point, the number is divided by 10 as follows:

$0.6=\frac{6}{10}$

Let's reduce the fraction:

$\frac{6:2}{10:2}=\frac{3}{5}$

Now we have two simple fractions with different denominators.

To compare them, note that the smallest common denominator between them is 15.

We'll multiply each one to reach the common denominator as follows:

$\frac{2}{3}\times\frac{5}{5}=\frac{10}{15}$

$\frac{3}{5}\times\frac{3}{3}=\frac{9}{15}$

Now we can compare the two fractions and see that:

$\frac{10}{15}>\frac{9}{15}$

Final Answer

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Key Points to Remember

Essential concepts to master this topic

Conversion: Transform decimal to fraction form for direct comparison
Common Denominator: Use LCD 15 to get $\frac{10}{15}$ vs $\frac{9}{15}$
Verify: Check that $\frac{2}{3} \approx 0.667 > 0.6$ by division ✓

Common Mistakes

Avoid these frequent errors

Comparing fractions with different denominators directly
Don't compare $\frac{2}{3}$ and $\frac{3}{5}$ by just looking at numerators = wrong conclusion! Different denominators make direct comparison impossible. Always convert to common denominators or decimal form first.

Practice Quiz

Test your knowledge with interactive questions

Which decimal number is greater?

FAQ

Everything you need to know about this question

Should I convert the fraction to decimal or the decimal to fraction?

Either method works! Converting 0.6 to $\frac{3}{5}$ often gives exact fractions that are easier to compare. Converting fractions to decimals works too, but might give long decimal approximations.

How do I find the common denominator between 3 and 5?

Find the Least Common Multiple (LCM) of the denominators. For 3 and 5, list multiples: 3, 6, 9, 12, 15 and 5, 10, 15. The LCM is 15!

Why can't I just cross-multiply to compare fractions?

Cross-multiplication works great! For $\frac{2}{3}$ vs $\frac{3}{5}$ , compare 2×5 = 10 and 3×3 = 9. Since 10 > 9, we have $\frac{2}{3} > \frac{3}{5}$ .

What if I get a messy decimal when converting fractions?

That's normal! $\frac{2}{3} = 0.666...$ (repeating). You only need enough decimal places to see which is larger. Here, 0.667 > 0.6 is clear.

Is there a faster way to compare these specific numbers?

Yes! Notice that 0.6 = 60% and $\frac{2}{3}$ = 66.7%. Thinking in percentages can make comparisons quicker and more intuitive.

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