Convert Fraction to Decimal: Solving 2/5 Step by Step

Q: Why do I multiply by 20/20 and not just 10/10?

Because 5 × 20 = 100, which gives us a clean denominator! Multiplying by $ \frac{10}{10} $ would give us $ \frac{20}{50} $, which is harder to convert to a decimal.

Q: Can I just divide 2 ÷ 5 directly?

Yes! Long division works too: 2 ÷ 5 = 0.4. The equivalent fraction method just makes it easier to see the pattern without doing division.

Q: How do I know which power of 10 to use?

Look at your denominator and think: "What times this number gives me 10, 100, or 1000?" Use the smallest power of 10 that works cleanly.

Q: Is 0.4 the same as 0.40?

Yes! Adding zeros after the decimal point doesn't change the value. Both 0.4 and 0.40 represent the same number.

Fraction to Decimal with Equivalent Fractions

Convert $\frac{2}{5}$ into a decimal.

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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 Change the denominator to any multiple of 10 and 10

00:06 Make sure to multiply both numerator and denominator

00:18 Convert to decimal fraction

00:21 When the denominator equals 10, place the numerator right after the decimal point

00:27 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

Convert $\frac{2}{5}$ into a decimal.

Step-by-step solution

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

Step 1: Convert the fraction by adjusting its denominator to a base of 100.
Step 2: Scale the fraction accordingly and compute the equivalent decimal.
Step 3: Compare to the given choices and confirm the result.

Let's work through these steps:
Step 1: We have the fraction $\frac{2}{5}$ . To convert 5 to 100, multiply both the numerator and the denominator by 20, because $5 \times 20 = 100$ .

Step 2: Multiply the numerator and denominator to get $\frac{40}{100}$ .

Step 3: The fraction $\frac{40}{100}$ can be written as a decimal:
$40$ divided by $100$ is equal to $0.4$ .

Therefore, the solution to the problem is 0.4.

Final Answer

0.4

Key Points to Remember

Essential concepts to master this topic

Rule: Convert denominator to power of 10 for easy decimal conversion
Technique: Multiply $\frac{2}{5}$ by $\frac{20}{20}$ to get $\frac{40}{100}$
Check: Verify that $\frac{40}{100} = 0.4$ equals original fraction ✓

Common Mistakes

Avoid these frequent errors

Converting denominators to wrong powers of 10
Don't just multiply by 10 to get $\frac{20}{50}$ = confusing decimal! This doesn't create a clean power of 10. Always find what number makes your denominator 10, 100, or 1000 for simple decimal conversion.

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 do I multiply by 20/20 and not just 10/10?

Because 5 × 20 = 100, which gives us a clean denominator! Multiplying by $\frac{10}{10}$ would give us $\frac{20}{50}$ , which is harder to convert to a decimal.

Can I just divide 2 ÷ 5 directly?

Yes! Long division works too: 2 ÷ 5 = 0.4. The equivalent fraction method just makes it easier to see the pattern without doing division.

What if my denominator doesn't go into 100 evenly?

Try 1000 instead! For example, $\frac{1}{3}$ becomes $\frac{333.33...}{1000}$ . Some fractions create repeating decimals like 0.333...

How do I know which power of 10 to use?

Look at your denominator and think: "What times this number gives me 10, 100, or 1000?" Use the smallest power of 10 that works cleanly.

Is 0.4 the same as 0.40?

Yes! Adding zeros after the decimal point doesn't change the value. Both 0.4 and 0.40 represent the same number.

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