If the value of Avogadro numberis `6.023xx10^(23)mol^(-1)` and the vaueof Boltzmann constant is `1.380xx10^(-23)JK^(-1)`, then the number of significant digits in the calculated value of the universal gas constant is

Explanation

To solve the problem of determining the number of significant digits in the calculated value of the universal gas constant (R), we will follow these steps:

### Step 1: Understand the relationship between the constants
The universal gas constant (R) can be calculated using the following relationship:
\[ R = k \times N_A \]
where:
- \( k \) is the Boltzmann constant
- \( N_A \) is Avogadro's number

### Step 2: Substitute the given values
We know:
- \( k = 1.380 \times 10^{-23} \, \text{J K}^{-1} \)
- \( N_A = 6.023 \times 10^{23} \, \text{mol}^{-1} \)

Now, substituting these values into the equation:
\[ R = (1.380 \times 10^{-23} \, \text{J K}^{-1}) \times (6.023 \times 10^{23} \, \text{mol}^{-1}) \]

### Step 3: Perform the multiplication
Calculating the multiplication:
1. Multiply the coefficients:
\[ 1.380 \times 6.023 = 8.31174 \]
2. Combine the powers of ten:
\[ 10^{-23} \times 10^{23} = 10^{0} = 1 \]

Thus, we have:
\[ R = 8.31174 \, \text{J K}^{-1} \text{mol}^{-1} \]

### Step 4: Determine the number of significant figures
Now, we need to determine the number of significant figures in the result \( 8.31174 \):
- The number \( 8.31174 \) has all non-zero digits and no leading or trailing zeros that would affect the count.
- Therefore, the significant figures in \( 8.31174 \) are counted as follows:
- All non-zero digits (8, 3, 1, 1, 7, 4) are significant.

Thus, the total number of significant figures in \( R \) is **6**.

### Final Answer
The number of significant digits in the calculated value of the universal gas constant \( R \) is **6**.

---