Convert Decimal 32.80 to Simplified Fraction Form

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

Count the decimal places! Since 32.80 has 2 decimal places, use 100 as the denominator. For 1 decimal place use 10, for 3 use 1000, and so on.

Q: Why do I need to simplify 80/100?

Fractions should always be in simplest form. The fraction 80/100 can be reduced by dividing both numerator and denominator by their greatest common divisor, which is 20.

Q: What if the decimal ends in zero like .80?

The trailing zero doesn't change the value! 0.80 = 0.8, but since we're converting the original decimal 32.80, we still use 80/100 and then simplify.

Q: How do I find the greatest common divisor quickly?

List factors or use the division method: 80 ÷ 20 = 4 and 100 ÷ 20 = 5, so GCD is 20. You can also start with obvious common factors like 2, 4, 5, or 10.

Q: Can I convert 32.80 to an improper fraction first?

Yes! Convert to $ \frac{3280}{100} $, simplify to $ \frac{164}{5} $, then convert to mixed number: $ 32\frac{4}{5} $. Both methods work!

Q: How can I check my answer is correct?

Convert back to decimal: $ 32\frac{4}{5} = 32 + 0.8 = 32.8 $. Since 32.8 = 32.80, your answer is correct!

Decimal Conversion with Mixed Number Simplification

Convert into a mixed fraction:

$32.80$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's write this as a reduced and simplified fraction.

00:09 Divide each digit after the decimal point by the place value it represents.

00:15 Next, place the correct denominator.

00:18 Don't forget to add thirty-two.

00:26 Reduce the fraction by dividing both the numerator and the denominator as much as you can.

00:46 And that's how you solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Convert into a mixed fraction:

$32.80$

Step-by-step solution

Let's write the decimal fraction as a mixed fraction.

Since there are 2 digits after the decimal point, we divide 80 by 100 and then 32, as follows:

$32+\frac{80}{100}$

Now let's divide the simple fraction by the highest number that can divide both the numerator and denominator, in this case the number is 20:

$32+\frac{80:20}{100:20}=32+\frac{4}{5}=32\frac{4}{5}$

Final Answer

$32\frac{4}{5}$

Key Points to Remember

Essential concepts to master this topic

Placement Rule: Count decimal places to determine denominator power of 10
Technique: Convert 32.80 = 32 + 80/100, then simplify fraction part
Check: Verify 4/5 = 0.80 when converted back to decimal ✓

Common Mistakes

Avoid these frequent errors

Forgetting to simplify the fraction part
Don't leave 32 80/100 as your final answer = incomplete simplification! The fraction 80/100 can be reduced further by dividing both parts by their GCD. Always find the greatest common divisor and reduce to lowest terms like 80÷20/100÷20 = 4/5.

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 the decimal part?

Count the decimal places! Since 32.80 has 2 decimal places, use 100 as the denominator. For 1 decimal place use 10, for 3 use 1000, and so on.

Why do I need to simplify 80/100?

Fractions should always be in simplest form. The fraction 80/100 can be reduced by dividing both numerator and denominator by their greatest common divisor, which is 20.

What if the decimal ends in zero like .80?

The trailing zero doesn't change the value! 0.80 = 0.8, but since we're converting the original decimal 32.80, we still use 80/100 and then simplify.

How do I find the greatest common divisor quickly?

List factors or use the division method: 80 ÷ 20 = 4 and 100 ÷ 20 = 5, so GCD is 20. You can also start with obvious common factors like 2, 4, 5, or 10.

Can I convert 32.80 to an improper fraction first?

Yes! Convert to $\frac{3280}{100}$ , simplify to $\frac{164}{5}$ , then convert to mixed number: $32\frac{4}{5}$ . Both methods work!

How can I check my answer is correct?

Convert back to decimal: $32\frac{4}{5} = 32 + 0.8 = 32.8$ . Since 32.8 = 32.80, your answer is correct!

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