The Rydberg's constant is `1.097373177xx10^(7)m^(-1)`. It can be expressed to three significant figure as

Options

A. `1.0974xx10^(7)m^(-1)`
B. `1.09xx10^(7)m^(-1)`
C. `1.10xx10^(7)m^(-1)`
D. `1.10^(7)m^(-1)`

Explanation

To express Rydberg's constant \(1.097373177 \times 10^{7} \, \text{m}^{-1}\) to three significant figures, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Significant Figures**:
The given value is \(1.097373177\). We need to identify the first three significant figures. The significant figures are the digits that contribute to its precision. In this case, the significant figures are:
- 1 (first digit)
- 0 (second digit)
- 9 (third digit)

2. **Round the Value**:
After identifying the first three significant figures (1, 0, and 9), we look at the next digit (which is 7) to determine if we need to round up. Since 7 is greater than 5, we round the last significant figure (9) up by 1.
- Rounding 9 up gives us 10.

3. **Adjust the Significant Figures**:
When we round 9 up to 10, we need to adjust the first digit accordingly. Therefore, the 1 becomes 2, and we need to carry over the 1 to the next digit.
- Thus, \(1.09\) becomes \(2.00\) when rounded correctly.

4. **Final Representation**:
Now we express the rounded number in scientific notation. The rounded value is \(2.00\), and since we need to maintain the exponent from the original number, we write:
\[ 1.10 \times 10^{7} \, \text{m}^{-1} \]

### Final Answer:
The Rydberg's constant expressed to three significant figures is:
\[ 1.10 \times 10^{7} \, \text{m}^{-1} \]