Convert Decimal 66.322 to Simplified Fraction: Step-by-Step Solution

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

Count the number of decimal places! For 66.322, there are 3 decimal places, so use $ \frac{322}{1000} $ (1 followed by 3 zeros).

Q: What's the easiest way to find the GCD to simplify?

Start by checking if both numbers are even (divisible by 2). For 322 and 1000, both are even, so divide by 2 repeatedly until you can't anymore. 322 ÷ 2 = 161, 1000 ÷ 2 = 500.

Q: Why can't I just write 66.322 as 66322/1000?

That would be an improper fraction, not a mixed number! The question asks for a mixed fraction, which separates the whole number part (66) from the fractional part.

Q: What if I get confused about which part goes where?

Remember: whole number stays whole, decimal part becomes the fraction. So 66.322 = 66 + 0.322, and 0.322 = $ \frac{322}{1000} $ simplified.

Decimal to Mixed Fraction with Simplification

Convert into a mixed fraction:

$66.322$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's write this as a reduced, simplified fraction.

00:09 Divide each number after the decimal by the number it stands for.

00:13 Make sure to place the correct denominator.

00:17 Don't forget to add 66, so keep that in mind.

00:32 Reduce the fraction as much as possible. Divide both the top and bottom numbers.

00:50 And that's how we find the solution to the problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Convert into a mixed fraction:

$66.322$

Step-by-step solution

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

Since there are 3 digits after the decimal point, we'll divide 322 by 1000 and 66, as follows:

$66+\frac{322}{1000}$

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 2:

$66+\frac{322:2}{1000:2}=36+\frac{161}{500}=66\frac{161}{500}$

Final Answer

$66\frac{161}{500}$

Key Points to Remember

Essential concepts to master this topic

Position Rule: Count decimal places to determine denominator power of 10
Technique: 66.322 = 66 + 322/1000, then find GCD of 322 and 1000
Check: Convert back: 66 + 161/500 = 66 + 0.322 = 66.322 ✓

Common Mistakes

Avoid these frequent errors

Not simplifying the fractional part to lowest terms
Don't leave 66 322/1000 as your final answer = unnecessarily complex fraction! This makes the answer harder to use and isn't in simplest form. Always find the GCD of numerator and denominator to reduce the fraction completely.

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 number of decimal places! For 66.322, there are 3 decimal places, so use $\frac{322}{1000}$ (1 followed by 3 zeros).

What's the easiest way to find the GCD to simplify?

Start by checking if both numbers are even (divisible by 2). For 322 and 1000, both are even, so divide by 2 repeatedly until you can't anymore. 322 ÷ 2 = 161, 1000 ÷ 2 = 500.

Why can't I just write 66.322 as 66322/1000?

That would be an improper fraction, not a mixed number! The question asks for a mixed fraction, which separates the whole number part (66) from the fractional part.

How do I check if 161 and 500 can be simplified further?

Check if they share any common factors. Since 161 is odd and 500 is even, they don't share the factor 2. Try other small primes like 3, 5, 7. Since 161 = 7 × 23 and 500 has no factors of 7 or 23, they're already simplified!

What if I get confused about which part goes where?

Remember: whole number stays whole, decimal part becomes the fraction. So 66.322 = 66 + 0.322, and 0.322 = $\frac{322}{1000}$ simplified.

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