A line segment of length 7.5 cm was wrongly measured as 7.2 cm. What was the error per cent ?

Answer

To solve the problem of finding the error percentage when a line segment of length 7.5 cm is wrongly measured as 7.2 cm, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Original and Measured Lengths**:
- Original Length (O) = 7.5 cm
- Measured Length (M) = 7.2 cm

2. **Calculate the Error**:
- Error (E) = Original Length - Measured Length
- E = 7.5 cm - 7.2 cm
- E = 0.3 cm

3. **Calculate the Error Percentage**:
- The formula for error percentage is:
\[ \text{Error Percentage} = \left(\frac{\text{Error}}{\text{Original Length}}\right) \times 100 \]
- Substitute the values into the formula:
\[ \text{Error Percentage} = \left(\frac{0.3 \text{ cm}}{7.5 \text{ cm}}\right) \times 100 \]

4. **Perform the Calculation**:
- First, calculate the fraction:
\[ \frac{0.3}{7.5} = 0.04 \]
- Now, multiply by 100 to get the percentage:
\[ 0.04 \times 100 = 4\% \]

5. **Final Result**:
- The error percentage is **4%**.