A line of length 1.5 metres was measured as 1.55 metres by mis take. What will be the value of error per cent ?

Options

A. 0.0005
B. 3 `7/31` %
C. 3 `1/3` %
D. 0.005

Answer

To solve the problem of finding the error percentage when a line of length 1.5 meters is mistakenly measured as 1.55 meters, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Original Length and Measured Length:**
- Original Length (O) = 1.5 meters
- Measured Length (M) = 1.55 meters

2. **Calculate the Error:**
- Error (E) = Measured Length - Original Length
- E = M - O = 1.55 m - 1.5 m = 0.05 m

3. **Calculate the Error Percentage:**
- Error Percentage (EP) is calculated using the formula:
\[ EP = \left( \frac{E}{O} \right) \times 100 \]
- Substitute the values:
\[ EP = \left( \frac{0.05}{1.5} \right) \times 100 \]

4. **Perform the Division:**
- Calculate \( \frac{0.05}{1.5} \):
\[ \frac{0.05}{1.5} = \frac{5}{150} = \frac{1}{30} \]

5. **Multiply by 100 to Get the Percentage:**
- Now, multiply by 100:
\[ EP = \left( \frac{1}{30} \right) \times 100 = \frac{100}{30} \approx 3.33\% \]

### Final Answer:
The error percentage is approximately **3.33%**.