Convert Mixed Number 3 4/200: Step-by-Step Decimal Transformation

Mixed Number Conversion with Large Denominators

34200= 3\frac{4}{200}=

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

34200= 3\frac{4}{200}=

2

Step-by-step solution

To solve this problem, we will follow these steps:

  • Step 1: Simplify the fraction 4200\frac{4}{200}.
  • Step 2: Convert the simplified fraction to a decimal.
  • Step 3: Combine this decimal with the whole number part, 33.

Now, let's work through these steps:

Step 1: Simplification
The fraction 4200\frac{4}{200} can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 4.

  • 4200=4÷4200÷4=150\frac{4}{200} = \frac{4 \div 4}{200 \div 4} = \frac{1}{50}

Step 2: Convert to Decimal
To convert 150\frac{1}{50} into a decimal, consider converting the fraction to have a power of 10 in the denominator. Multiply both numerator and denominator by 2:

  • 150=1×250×2=2100\frac{1}{50} = \frac{1 \times 2}{50 \times 2} = \frac{2}{100}
  • The decimal form for 2100\frac{2}{100} is 0.020.02. This is because dividing 2 by 100 gives 0.02.

Step 3: Combine with Whole Number
Add the decimal 0.020.02 to the whole number 33:

  • 3+0.02=3.023 + 0.02 = 3.02

Therefore, the decimal form of 342003 \frac{4}{200} is 3.023.02.

3

Final Answer

3.02 3.02

Key Points to Remember

Essential concepts to master this topic
  • Simplification: Always reduce fractions using greatest common divisor first
  • Technique: Convert 4200=150=2100=0.02 \frac{4}{200} = \frac{1}{50} = \frac{2}{100} = 0.02
  • Check: Verify 3+0.02=3.02 3 + 0.02 = 3.02 matches original mixed number ✓

Common Mistakes

Avoid these frequent errors
  • Converting without simplifying the fraction first
    Don't convert 4/200 directly to decimal by dividing 4 ÷ 200 = 0.02 without simplifying! While this gives the right answer, it makes calculations harder and you miss the pattern. Always simplify 4/200 = 1/50 first, then convert to make the work cleaner.

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 do I need to simplify 4/200 before converting to decimal?

+

Simplifying makes the math much easier! 4200=150 \frac{4}{200} = \frac{1}{50} is simpler to work with. You can then easily see that 150=2100=0.02 \frac{1}{50} = \frac{2}{100} = 0.02 .

How do I find the greatest common divisor of 4 and 200?

+

List the factors! Factors of 4: 1, 2, 4. Factors of 200: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200. The largest number in both lists is 4, so GCD = 4.

Can I convert 1/50 to decimal without making it 2/100?

+

Yes! You can divide directly: 1÷50=0.02 1 ÷ 50 = 0.02 . However, converting to 2100 \frac{2}{100} first makes it easier to see the decimal pattern since 100 is a power of 10.

What if the mixed number has a bigger whole number part?

+

The process is exactly the same! For example: 154200=15+0.02=15.02 15\frac{4}{200} = 15 + 0.02 = 15.02 . Always convert the fraction part to decimal first, then add it to the whole number.

How do I check if 3.02 is really equal to the original mixed number?

+

Convert back! Take 3.02: the whole number is 3, and 0.02 = 2100=150=4200 \frac{2}{100} = \frac{1}{50} = \frac{4}{200} . So 3.02 = 34200 3\frac{4}{200} ✓

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Decimal Fractions - Basic questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations