A student in the laboratory measures thickness of a wire using screw gauge. The readings are 1.22 mm, 1.23 mm, 1.19 mm and 1.20 mm. The percentage error is `(x)/(121)%`. The value x is _______.

Explanation

To solve the problem of calculating the percentage error in the measurement of the thickness of a wire using a screw gauge, we will follow these steps:

### Step 1: Calculate the Average Thickness
The readings taken by the student are:
- 1.22 mm
- 1.23 mm
- 1.19 mm
- 1.20 mm

To find the average thickness, we add all the readings together and divide by the number of readings (4).

\[ \text{Average Thickness} = \frac{1.22 + 1.23 + 1.19 + 1.20}{4} \]

Calculating this:

\[ \text{Average Thickness} = \frac{4.84}{4} = 1.21 \text{ mm} \]

### Step 2: Calculate the Absolute Errors
Next, we will calculate the absolute error for each reading by taking the difference between each reading and the average thickness.

1. For 1.22 mm:
\[ |1.22 - 1.21| = 0.01 \text{ mm} \]

2. For 1.23 mm:
\[ |1.23 - 1.21| = 0.02 \text{ mm} \]

3. For 1.19 mm:
\[ |1.19 - 1.21| = 0.02 \text{ mm} \]

4. For 1.20 mm:
\[ |1.20 - 1.21| = 0.01 \text{ mm} \]

### Step 3: Calculate the Mean Absolute Error
Now, we find the mean of these absolute errors:

\[ \text{Mean Absolute Error} = \frac{0.01 + 0.02 + 0.02 + 0.01}{4} = \frac{0.06}{4} = 0.015 \text{ mm} \]

### Step 4: Calculate the Percentage Error
The percentage error is calculated using the formula:

\[ \text{Percentage Error} = \left(\frac{\text{Mean Absolute Error}}{\text{Average Thickness}}\right) \times 100 \]

Substituting the values we calculated:

\[ \text{Percentage Error} = \left(\frac{0.015}{1.21}\right) \times 100 \]

Calculating this gives:

\[ \text{Percentage Error} \approx 1.24\% \]

### Step 5: Relate to Given Percentage Error
The problem states that the percentage error can be expressed as \(\frac{x}{121}\%\). Therefore, we set up the equation:

\[ 1.24 = \frac{x}{121} \]

To find \(x\), we multiply both sides by 121:

\[ x = 1.24 \times 121 \approx 150 \]

### Final Answer
Thus, the value of \(x\) is:

\[ \boxed{150} \]