Compare Fractions and Decimals: Is 1/3 >, <, or = to 0.3?

Fraction Comparison with Common Denominators

Choose the appropriate sign:

13?0.3 \frac{1}{3}?0.3

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Choose the appropriate sign
00:05 Convert decimal number to fraction
00:18 Multiply each fraction by the second denominator to find the common denominator
00:22 Make sure to multiply numerator by numerator and denominator by denominator
00:34 Now let's compare the fractions
00:41 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Choose the appropriate sign:

13?0.3 \frac{1}{3}?0.3

2

Step-by-step solution

First, let's convert 0.3 to a simple fraction.

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

0.3=310 0.3=\frac{3}{10}

Now we have two simple fractions with different denominators.

To compare them, note that the smallest common denominator between them is 30.

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

13×1010=1030 \frac{1}{3}\times\frac{10}{10}=\frac{10}{30}

310×33=930 \frac{3}{10}\times\frac{3}{3}=\frac{9}{30}

Now we can compare the two fractions and see that:

1030>930 \frac{10}{30}>\frac{9}{30}

3

Final Answer

> >

Key Points to Remember

Essential concepts to master this topic
  • Rule: Convert fractions to common denominators before comparing
  • Technique: 13=1030 \frac{1}{3} = \frac{10}{30} and 0.3=930 0.3 = \frac{9}{30}
  • Check: Compare numerators: 10 > 9, so 13>0.3 \frac{1}{3} > 0.3

Common Mistakes

Avoid these frequent errors
  • Comparing decimals and fractions without converting
    Don't compare 1/3 to 0.3 directly = wrong answer! The different forms hide their true relationship. Always convert both to the same format (both fractions or both decimals) before comparing.

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 1/3 and 0.3 directly?

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Because they're in different formats! It's like comparing apples to oranges. You need to convert them to the same format first - either both as fractions or both as decimals.

How do I know which common denominator to use?

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Find the Least Common Multiple (LCM) of the denominators. For 3 and 10, the LCM is 30. You can also use any common multiple, but the LCM keeps numbers smaller and easier to work with.

Can I convert 1/3 to a decimal instead?

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Yes! 13=0.333... \frac{1}{3} = 0.333... Since 0.333... > 0.3, you get the same answer. However, be careful with repeating decimals - sometimes fractions are more precise.

What if the fractions have the same denominator already?

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Lucky you! When denominators are the same, just compare the numerators. The fraction with the larger numerator is the larger fraction.

How do I multiply fractions to get common denominators?

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Multiply both the numerator and denominator by the same number. For 13 \frac{1}{3} , multiply by 1010 \frac{10}{10} to get 1030 \frac{10}{30} . This doesn't change the fraction's value!

Is there a shortcut for comparing fractions?

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Yes! You can cross-multiply: Compare 13 \frac{1}{3} and 310 \frac{3}{10} by calculating 1×10 = 10 and 3×3 = 9. Since 10 > 9, we know 13>310 \frac{1}{3} > \frac{3}{10} .

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