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

To solve this problem, we will follow these steps:

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

Now, let's work through these steps:

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

• $\frac{4}{200} = \frac{4 \div 4}{200 \div 4} = \frac{1}{50}$

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

• $\frac{1}{50} = \frac{1 \times 2}{50 \times 2} = \frac{2}{100}$
• The decimal form for $\frac{2}{100}$ is $0.02$. This is because dividing 2 by 100 gives 0.02.

Step 3: Combine with Whole Number
Add the decimal $0.02$ to the whole number $3$:

• $3 + 0.02 = 3.02$

Therefore, the decimal form of $3 \frac{4}{200}$ is $3.02$.