Convert 3.09 to Complex Fraction: Decimal Transformation Problem

Q: Why is the denominator 100 and not 10?

The denominator comes from counting decimal places. Since 0.09 has two decimal places, we use 100 (which has two zeros). One decimal place = 10, two decimal places = 100, three decimal places = 1000.

Q: What if the decimal doesn't simplify?

That's okay! $ \frac{9}{100} $ is already in simplest form because 9 and 100 don't share any common factors except 1. Always check if you can reduce, but don't worry if you can't.

Q: How do I know I have the right mixed number?

Convert your mixed number back to a decimal! $ 3\frac{9}{100} = 3 + 0.09 = 3.09 $. If you get the original decimal, your answer is correct.

Q: Can I write this as an improper fraction instead?

Yes! $ 3\frac{9}{100} = \frac{309}{100} $. But the question asks for a complex fraction (mixed number), so stick with $ 3\frac{9}{100} $.

Q: What if I get confused about which part is the whole number?

The whole number is everything before the decimal point. In 3.09, the whole number is 3. The decimal part (0.09) becomes your fraction.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert to complex fraction

00:03 First we'll convert to fraction

00:06 The denominator depends on the number of digits after the decimal point

00:09 There are 2 digits, so the denominator will be 100

00:13 We'll place the digits as a whole number in the numerator

00:23 We'll break down 309 to 300 and 9

00:31 Break down the fraction into 2 fractions, the whole fraction and the remainder

00:40 We'll reduce what's possible

00:51 We'll combine into a complex fraction

00:57 And that's the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

Convert 3.09 to a complex fraction

2

Step-by-step solution

To convert the decimal number 3.09 into a complex fraction, let's proceed step-by-step:

Step 1: Separate the whole number and the decimal fraction. Here, we have the whole number $3$ and the decimal fraction $0.09$ .
Step 2: Convert the decimal fraction to a simple fraction. Since the decimal $0.09$ has two decimal places, it is equivalent to $\frac{9}{100}$ .
Step 3: Combine the whole number and the fraction. Now, we express 3.09 as the mixed number $3 \frac{9}{100}$ .

Therefore, the complex fractional representation of 3.09 is $3\frac{9}{100}$ .

3

Final Answer

$3\frac{9}{100}$

Key Points to Remember

Essential concepts to master this topic

Place Value Rule: Decimal places determine the denominator (hundredths = 100)
Technique: Convert 0.09 to $\frac{9}{100}$ using two decimal places
Check: Verify $3\frac{9}{100} = 3.09$ by converting back ✓

Common Mistakes

Avoid these frequent errors

Using wrong denominator based on decimal places
Don't count the 3 as a decimal place and write $3\frac{9}{1000}$ = wrong answer! Only the digits after the decimal point determine place value. Always count decimal places correctly: 0.09 has 2 places, so denominator is 100.

Practice Quiz

Test your knowledge with interactive questions

How much of the whole does the shaded area (blue) represent?

FAQ

Everything you need to know about this question

Why is the denominator 100 and not 10?

+

The denominator comes from counting decimal places. Since 0.09 has two decimal places, we use 100 (which has two zeros). One decimal place = 10, two decimal places = 100, three decimal places = 1000.

What if the decimal doesn't simplify?

+

That's okay! $\frac{9}{100}$ is already in simplest form because 9 and 100 don't share any common factors except 1. Always check if you can reduce, but don't worry if you can't.

How do I know I have the right mixed number?

+

Convert your mixed number back to a decimal! $3\frac{9}{100} = 3 + 0.09 = 3.09$ . If you get the original decimal, your answer is correct.

Can I write this as an improper fraction instead?

+

Yes! $3\frac{9}{100} = \frac{309}{100}$ . But the question asks for a complex fraction (mixed number), so stick with $3\frac{9}{100}$ .

What if I get confused about which part is the whole number?

+

The whole number is everything before the decimal point. In 3.09, the whole number is 3. The decimal part (0.09) becomes your fraction.

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Convert 3.09 to Complex Fraction: Decimal Transformation Problem

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