If the percentage errors of `A,B,and C` are `a, b, and c,` respectively ,then the total percentage error in the product `ABC` is

Options

A. `abc`
B. ` a + b + c`
C. `(1)/(a) + (1)/(b) +(1)/( c )`
D. `ab + bc+ ca`

Explanation

To solve the problem of finding the total percentage error in the product \( ABC \) given the percentage errors of \( A, B, \) and \( C \) as \( a, b, \) and \( c \) respectively, we can follow these steps:

### Step 1: Understand the concept of percentage error
The percentage error in a measurement is defined as the ratio of the absolute error to the measured value, multiplied by 100. For small errors, when multiplying or dividing quantities, the total percentage error can be found by adding the individual percentage errors.

### Step 2: Identify the given percentage errors
From the problem, we know:
- Percentage error in \( A \) is \( a \% \)
- Percentage error in \( B \) is \( b \% \)
- Percentage error in \( C \) is \( c \% \)

### Step 3: Apply the property of errors for multiplication
When multiplying quantities, the total percentage error in the product is the sum of the individual percentage errors. Therefore, for the product \( ABC \), the total percentage error can be expressed as:
\[ \text{Total Percentage Error in } ABC = a + b + c \]

### Step 4: Write the final answer
Thus, the total percentage error in the product \( ABC \) is:
\[ \text{Total Percentage Error} = a + b + c \]

### Conclusion
The total percentage error in the product \( ABC \) is the sum of the individual percentage errors of \( A, B, \) and \( C \).

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