Convert Decimal 3.08: Finding Alternative Number Representations

Q: Why can't I just write 3.08 as 3 and 8/100?

You can start that way, but 8/100 isn't simplified! Mixed numbers should always have fractions in lowest terms. Divide both numerator and denominator by their GCD (4) to get $ \frac{2}{25} $.

Q: What if the decimal has more places like 3.125?

Same process! 3.125 = $ 3\frac{125}{1000} $. Find GCD of 125 and 1000 (which is 125), then simplify to $ 3\frac{1}{8} $.

Q: How can I check if my mixed number is correct?

Convert back to decimal! $ 3\frac{2}{25} = 3 + \frac{2}{25} = 3 + 0.08 = 3.08 $. If you get your original decimal, you're right!

Q: Why do we need mixed numbers when decimals are easier?

Mixed numbers show exact values without rounding! Some fractions like $ \frac{1}{3} $ become repeating decimals (0.333...), but mixed numbers keep them precise.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert to mixed fraction

00:03 Break down the number into whole number and remainder

00:12 Convert the remainder to fraction

00:20 Reduce the fraction, make sure to divide both numerator and denominator

00:28 Add to mixed fraction

00:34 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$3.08=$

2

Step-by-step solution

To solve the problem of converting $3.08$ to a mixed fraction, follow these steps:

Step 1: Identify the whole number
The given decimal $3.08$ has a whole number part, which is $3$ .
Step 2: Convert the decimal part to a fraction
The decimal part is $0.08$ . To convert $0.08$ to a fraction, recognize that it represents $\frac{8}{100}$ , as 8 is in the hundredths place.
Step 3: Simplify the fraction
Simplify $\frac{8}{100}$ by finding the greatest common divisor of 8 and 100, which is 4. Divide both the numerator and the denominator by 4: $\frac{8 \div 4}{100 \div 4} = \frac{2}{25}$ .
Step 4: Combine the whole number with the fraction
Thus, $3.08$ can be expressed as $3 \frac{2}{25}$ .

The correct answer is therefore $3\frac{2}{25}$ .

3

Final Answer

$3\frac{2}{25}$

Key Points to Remember

Essential concepts to master this topic

Rule: Place decimal digits over corresponding place values
Technique: Convert 0.08 to $\frac{8}{100}$ then simplify by GCD
Check: Verify $3\frac{2}{25} = 3 + \frac{2}{25} = 3.08$ ✓

Common Mistakes

Avoid these frequent errors

Not simplifying the fraction part
Don't leave $3\frac{8}{100}$ as your final answer = incorrect simplified form! This isn't in lowest terms and shows incomplete understanding. Always find the GCD and reduce the fraction to simplest form.

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

Why can't I just write 3.08 as 3 and 8/100?

+

You can start that way, but 8/100 isn't simplified! Mixed numbers should always have fractions in lowest terms. Divide both numerator and denominator by their GCD (4) to get $\frac{2}{25}$ .

How do I find the greatest common divisor quickly?

+

List factors of both numbers: 8 has factors 1, 2, 4, 8 and 100 has factors 1, 2, 4, 5, 10, 20, 25, 50, 100. The largest common factor is 4!

What if the decimal has more places like 3.125?

+

Same process! 3.125 = $3\frac{125}{1000}$ . Find GCD of 125 and 1000 (which is 125), then simplify to $3\frac{1}{8}$ .

How can I check if my mixed number is correct?

+

Convert back to decimal! $3\frac{2}{25} = 3 + \frac{2}{25} = 3 + 0.08 = 3.08$ . If you get your original decimal, you're right!

Why do we need mixed numbers when decimals are easier?

+

Mixed numbers show exact values without rounding! Some fractions like $\frac{1}{3}$ become repeating decimals (0.333...), but mixed numbers keep them precise.

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Convert Decimal 3.08: Finding Alternative Number Representations

Decimal to Mixed Number with Simplification

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