Convert Mixed Number: Express 1 2/5 as Decimal

Q: Why can't I just divide 2 by 5 directly?

You absolutely can! Dividing 2 ÷ 5 = 0.4 is actually the fastest method. Converting to tenths first just helps you see why it works step by step.

Q: What if the fraction doesn't convert to a nice decimal?

Some fractions like $ \frac{1}{3} $ give repeating decimals (0.333...). In these cases, you can use long division or express as a rounded decimal depending on what's asked.

Q: How do I know if 1.4 is really correct?

Convert back! 1.4 = 1 + 0.4, and 0.4 = $ \frac{4}{10} = \frac{2}{5} $. So you get $ 1\frac{2}{5} $ - exactly what you started with!

Q: Is there a pattern for converting fifths to decimals?

Yes! Fifths always convert nicely: $ \frac{1}{5} = 0.2 $, $ \frac{2}{5} = 0.4 $, $ \frac{3}{5} = 0.6 $, $ \frac{4}{5} = 0.8 $. They increase by 0.2 each time!

Q: What's the difference between 1.2 and 1.4 in this problem?

The wrong answer 1.2 comes from converting $ \frac{2}{5} $ incorrectly as $ \frac{2}{10} = 0.2 $. But $ \frac{2}{5} $ actually equals $ \frac{4}{10} = 0.4 $, giving us 1.4.

Mixed Number Conversion with Decimal Form

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert to decimal fraction

00:03 Break down into whole number and fraction

00:07 Convert from whole number to proper fraction

00:11 Add with common denominator

00:16 Change the fraction so the denominator is 10

00:18 Make sure to multiply both numerator and denominator

00:24 Convert from fraction to decimal fraction

00:30 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

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

Step-by-step solution

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

Step 1: Convert the fraction part of the mixed number $\frac{2}{5}$ to a decimal.
Step 2: Add this decimal to the whole number part.

Now, let's work through each step:
Step 1: Convert $\frac{2}{5}$ to an equivalent fraction with a denominator of 10. Multiply both the numerator and the denominator by 2:
$\frac{2 \times 2}{5 \times 2} = \frac{4}{10}$ This means $\frac{2}{5} = 0.4$ .

Step 2: Add the decimal 0.4 to the whole number part 1:
$1 + 0.4 = 1.4$

Therefore, the solution to the problem is $1.4$ .

Final Answer

$1.4$

Key Points to Remember

Essential concepts to master this topic

Rule: Mixed numbers equal whole number plus fraction in decimal form
Technique: Convert $\frac{2}{5}$ by multiplying by 2 to get $\frac{4}{10} = 0.4$
Check: Verify that 1 + 0.4 = 1.4 equals original mixed number ✓

Common Mistakes

Avoid these frequent errors

Adding denominators to whole numbers
Don't add 1 + 2 + 5 = 8 when converting mixed numbers! This treats parts incorrectly and gives wrong decimal values. Always convert the fraction part to decimal first, then add to the whole number.

Practice Quiz

Test your knowledge with interactive questions

Convert into fraction form:

$$ 0.38= $$

FAQ

Everything you need to know about this question

Why can't I just divide 2 by 5 directly?

You absolutely can! Dividing 2 ÷ 5 = 0.4 is actually the fastest method. Converting to tenths first just helps you see why it works step by step.

What if the fraction doesn't convert to a nice decimal?

Some fractions like $\frac{1}{3}$ give repeating decimals (0.333...). In these cases, you can use long division or express as a rounded decimal depending on what's asked.

How do I know if 1.4 is really correct?

Convert back! 1.4 = 1 + 0.4, and 0.4 = $\frac{4}{10} = \frac{2}{5}$ . So you get $1\frac{2}{5}$ - exactly what you started with!

Is there a pattern for converting fifths to decimals?

Yes! Fifths always convert nicely: $\frac{1}{5} = 0.2$ , $\frac{2}{5} = 0.4$ , $\frac{3}{5} = 0.6$ , $\frac{4}{5} = 0.8$ . They increase by 0.2 each time!

What's the difference between 1.2 and 1.4 in this problem?

The wrong answer 1.2 comes from converting $\frac{2}{5}$ incorrectly as $\frac{2}{10} = 0.2$ . But $\frac{2}{5}$ actually equals $\frac{4}{10} = 0.4$ , giving us 1.4.

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