Convert Decimal to Fraction: Simplifying 0.5 to Lowest Terms

Q: How do I know what denominator to use for a decimal?

Count the decimal places! One decimal place means denominator 10, two places means 100, three places means 1000, and so on.

Q: Can I convert 0.5 directly to 1/2 without writing 5/10 first?

Yes, with practice! But when learning, it's safer to write the decimal over the power of 10 first, then simplify. This prevents mistakes with more complex decimals.

Q: How can I check if my fraction is fully simplified?

A fraction is in lowest terms when the numerator and denominator share no common factors except 1. For $ \frac{1}{2} $, the only common factor is 1, so it's fully simplified!

Q: What if I get confused about place values?

Remember: the first digit after the decimal is tenths, second is hundredths, third is thousandths. So 0.5 has 5 in the tenths place = $ \frac{5}{10} $.

Fraction Conversion with Decimal Place Values

Write the following decimal fraction as a simple fraction and simplify:

$0.5=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Write it as a simple and reduced fraction

00:03 Divide each digit after the decimal point by the division amount it represents

00:10 Place the appropriate denominator

00:19 Reduce as much as possible, make sure to divide both numerator and denominator

00:31 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 the following decimal fraction as a simple fraction and simplify:

$0.5=$

Step-by-step solution

Since there is one digit after the decimal point, we divide 5 by 10:

$\frac{5}{10}$

Now let's find the highest number that divides both the numerator and the denominator.

In this case, the number is 5, so:

$\frac{5:5}{10:5}=\frac{1}{2}$

Final Answer

$\frac{1}{2}$

Key Points to Remember

Essential concepts to master this topic

Rule: Place decimal digits over powers of ten based on position
Technique: One decimal place means denominator 10, so $0.5 = \frac{5}{10}$
Check: Divide numerator by denominator: $1 ÷ 2 = 0.5$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to simplify the fraction to lowest terms
Don't leave $\frac{5}{10}$ as your final answer = incomplete solution! This fraction can be reduced further by dividing both numerator and denominator by their greatest common factor. Always find the GCF and simplify to get $\frac{1}{2}$ .

Practice Quiz

Test your knowledge with interactive questions

Reduce the following fraction:

$$ 0.30 $$

FAQ

Everything you need to know about this question

How do I know what denominator to use for a decimal?

Count the decimal places! One decimal place means denominator 10, two places means 100, three places means 1000, and so on.

What's the greatest common factor of 5 and 10?

List the factors: 5 has factors 1, 5 and 10 has factors 1, 2, 5, 10. The greatest common factor is 5, so divide both numerator and denominator by 5.

Can I convert 0.5 directly to 1/2 without writing 5/10 first?

Yes, with practice! But when learning, it's safer to write the decimal over the power of 10 first, then simplify. This prevents mistakes with more complex decimals.

How can I check if my fraction is fully simplified?

A fraction is in lowest terms when the numerator and denominator share no common factors except 1. For $\frac{1}{2}$ , the only common factor is 1, so it's fully simplified!

What if I get confused about place values?

Remember: the first digit after the decimal is tenths, second is hundredths, third is thousandths. So 0.5 has 5 in the tenths place = $\frac{5}{10}$ .

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