Perform the following calculations to the appropriate number of signficiant digits `(6.02xx10^(23)xx4.00)/(4.0xx10^(20))`

Answer

To solve the problem \((6.02 \times 10^{23} \times 4.00) / (4.0 \times 10^{20})\) and express the answer to the appropriate number of significant digits, we will follow these steps:

### Step 1: Identify the significant figures
- The number \(6.02\) has **three significant figures**.
- The number \(4.00\) has **four significant figures**.
- The number \(4.0\) has **two significant figures**.

The least number of significant figures among these is **two**, from \(4.0\).

### Step 2: Rewrite the expression
We can rewrite the expression as:
\[ \frac{(6.02 \times 10^{23}) \times (4.00)}{(4.0 \times 10^{20})} \]

### Step 3: Simplify the expression
First, we can simplify the powers of ten:
\[ = (6.02 \times 4.00) \times \frac{10^{23}}{10^{20}} \]
Using the property of exponents, we know that:
\[ \frac{10^{23}}{10^{20}} = 10^{23-20} = 10^{3} \]
Thus, we can rewrite the expression as:
\[ (6.02 \times 4.00) \times 10^{3} \]

### Step 4: Perform the multiplication
Now, we calculate \(6.02 \times 4.00\):
\[ 6.02 \times 4.00 = 24.08 \]

### Step 5: Adjust for significant figures
Since we are limited by the number with the least significant figures (which is \(4.0\) with **two significant figures**), we need to round \(24.08\) to two significant figures:
- The first two significant digits in \(24.08\) are \(2\) and \(4\).
- The next digit is \(0\), which is less than \(5\), so we do not round up.

Thus, \(24.08\) rounded to two significant figures is:
\[ 24 \times 10^{3} \]

### Step 6: Final answer in scientific notation
Expressing this in proper scientific notation, we have:
\[ 2.4 \times 10^{4} \]

### Conclusion
The final answer, expressed with the appropriate number of significant digits, is:
\[ \boxed{2.4 \times 10^{4}} \]