Convert Mixed Number: Expressing 4⅖ as a Decimal

Q: Why can't I just divide 2 by 5 to get the decimal?

You absolutely can! Division is another correct method: $ 2 \div 5 = 0.4 $. Both scaling to tenths (like in the explanation) and division give the same answer.

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

Some fractions create repeating decimals. For example, $ \frac{1}{3} = 0.333... $ You can round to a reasonable number of decimal places or leave it as a fraction.

Q: How do I know what to multiply by to get tenths or hundredths?

Look at the denominator! To get tenths, see what makes the denominator 10. To get hundredths, see what makes it 100. For $ \frac{2}{5} $, multiply by 2 to get $ \frac{4}{10} $.

Q: Can I convert the whole mixed number at once?

Yes! You can use the formula: mixed number = (whole × denominator + numerator) ÷ denominator. For $ 4\frac{2}{5} $: (4×5+2)÷5 = 22÷5 = 4.4

Q: What's the difference between 4.4 and 4.40?

They're exactly the same value! The extra zero doesn't change the number. However, 4.40 might indicate more precision in measurement contexts.

Mixed Number Conversion with Fraction-to-Decimal

$4\frac{2}{5}=$

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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 We want to convert from fraction to decimal fraction, so we'll change the denominator to 10

00:11 Make sure to multiply both numerator and denominator

00:25 Convert fraction to decimal fraction

00:30 Add

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

$4\frac{2}{5}=$

Step-by-step solution

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

Step 1: Convert the fractional part $\frac{2}{5}$ to a decimal by scaling the fraction.
Step 2: Add the decimal from the fraction to the whole number.

Let's go through each step in detail:
Step 1: Convert $\frac{2}{5}$ to have a denominator of 10.
To do this, multiply both the numerator and the denominator by 2:

$\frac{2 \times 2}{5 \times 2} = \frac{4}{10}$

This fraction, $\frac{4}{10}$ , is equivalent to the decimal $0.4$ .

Step 2: Add this decimal to the whole number $4$ :
$4 + 0.4 = 4.4$

Therefore, the decimal representation of $4\frac{2}{5}$ is $4.4$ .

Final Answer

$4.4$

Key Points to Remember

Essential concepts to master this topic

Rule: Convert the fraction part to decimal, then add to whole
Technique: Scale $\frac{2}{5}$ to $\frac{4}{10} = 0.4$
Check: Verify 4.4 = 4 + 0.4 where 0.4 = 2/5 ✓

Common Mistakes

Avoid these frequent errors

Adding the fraction directly without converting
Don't just write 4 + 2/5 = 4.25! This treats the fraction as if it's hundredths instead of fifths. Always convert the fraction to its decimal equivalent first, then add to the whole number.

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 can't I just divide 2 by 5 to get the decimal?

You absolutely can! Division is another correct method: $2 \div 5 = 0.4$ . Both scaling to tenths (like in the explanation) and division give the same answer.

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

Some fractions create repeating decimals. For example, $\frac{1}{3} = 0.333...$ You can round to a reasonable number of decimal places or leave it as a fraction.

How do I know what to multiply by to get tenths or hundredths?

Look at the denominator! To get tenths, see what makes the denominator 10. To get hundredths, see what makes it 100. For $\frac{2}{5}$ , multiply by 2 to get $\frac{4}{10}$ .

Can I convert the whole mixed number at once?

Yes! You can use the formula: mixed number = (whole × denominator + numerator) ÷ denominator. For $4\frac{2}{5}$ : (4×5+2)÷5 = 22÷5 = 4.4

What's the difference between 4.4 and 4.40?

They're exactly the same value! The extra zero doesn't change the number. However, 4.40 might indicate more precision in measurement contexts.

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