Convert Decimal to Fraction: Express 0.4 in Fractional Form

Q: How do I know what denominator to use?

Count the decimal places! One decimal place (like 0.4) uses denominator 10, two decimal places (like 0.25) uses 100, and so on. Each place adds another zero!

Q: Is 4/10 wrong as an answer?

$ \frac{4}{10} $ equals 0.4, so it's mathematically correct! However, most teachers want the simplest form, which is $ \frac{2}{5} $. Always simplify unless told otherwise.

Q: How can I check if my fraction is correct?

Divide the numerator by the denominator: $ 2 \div 5 = 0.4 $. If you get back to your original decimal, your fraction is right!

Q: What does GCD mean exactly?

GCD (Greatest Common Divisor) is the largest number that divides evenly into both the numerator and denominator. For 4 and 10, the GCD is 2 because 2 is the biggest number that goes into both.

Decimal to Fraction with Simplification

Write 0.4 as a fraction.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert to a simple and reduced fraction

00:03 Place the numbers in the denominator

00:06 Move the decimal point right until the number is whole and not decimal

00:09 We moved once, so the denominator will be equal to 10

00:15 Now let's reduce as much as possible

00:20 Break down 4 into factors 2 and 2, and 10 into factors 5 and 2

00:23 Reduce what we can

00:28 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

Write 0.4 as a fraction.

Step-by-step solution

To convert the decimal 0.4 to a fraction, follow these steps:

Step 1: Write the decimal as a fraction.

0.4 as a fraction is $\frac{4}{10}$ because there is one digit after the decimal point.

Step 2: Simplify the fraction.

To simplify $\frac{4}{10}$ , find the greatest common divisor (GCD) of 4 and 10, which is 2.

Divide both the numerator and the denominator by their GCD:

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

Therefore, the fraction $\frac{4}{10}$ simplifies to $\frac{2}{5}$ .

Thus, the decimal 0.4 can be expressed as the fraction $\frac{2}{5}$ .

Final Answer

$\frac{2}{5}$

Key Points to Remember

Essential concepts to master this topic

Place Value: One decimal place means denominator of 10
Technique: Write $\frac{4}{10}$ then find GCD of 4 and 10
Check: Divide 2 by 5 to get 0.4 again ✓

Common Mistakes

Avoid these frequent errors

Forgetting to simplify the fraction
Don't leave $\frac{4}{10}$ as your final answer = unsimplified form! This isn't wrong mathematically, but it's not in simplest form. Always find the GCD and divide both numerator and denominator by it to get $\frac{2}{5}$ .

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

How do I know what denominator to use?

Count the decimal places! One decimal place (like 0.4) uses denominator 10, two decimal places (like 0.25) uses 100, and so on. Each place adds another zero!

What if I can't find the GCD easily?

Try dividing both numbers by small primes like 2, 3, or 5. For 4 and 10, both divide by 2. You can also list factors: 4: 1, 2, 4 and 10: 1, 2, 5, 10. The largest common factor is 2.

Is 4/10 wrong as an answer?

$\frac{4}{10}$ equals 0.4, so it's mathematically correct! However, most teachers want the simplest form, which is $\frac{2}{5}$ . Always simplify unless told otherwise.

How can I check if my fraction is correct?

Divide the numerator by the denominator: $2 \div 5 = 0.4$ . If you get back to your original decimal, your fraction is right!

What does GCD mean exactly?

GCD (Greatest Common Divisor) is the largest number that divides evenly into both the numerator and denominator. For 4 and 10, the GCD is 2 because 2 is the biggest number that goes into both.

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