The length of a rod is 22.4 m out of it 2.543m is cut out. The remaining length of the rod according to the idea of significant figures is

Options

A. 19.8 m
B. 19.9m
C. 20.0 mn
D. 19.86 m

Answer

To find the remaining length of the rod after cutting out a portion, we will follow these steps:

### Step 1: Identify the lengths involved
We are given:
- The original length of the rod, \( L = 22.4 \, \text{m} \)
- The length cut out, \( L_1 = 2.543 \, \text{m} \)

### Step 2: Calculate the remaining length
To find the remaining length of the rod, we subtract the length cut out from the original length:
\[ L_2 = L - L_1 \]
Substituting the values:
\[ L_2 = 22.4 \, \text{m} - 2.543 \, \text{m} \]

### Step 3: Perform the subtraction
Now, we perform the calculation:
\[ L_2 = 22.4 - 2.543 = 19.857 \, \text{m} \]

### Step 4: Determine the significant figures
Next, we need to express the remaining length with the correct number of significant figures. The original length \( 22.4 \, \text{m} \) has 3 significant figures, and \( 2.543 \, \text{m} \) has 4 significant figures. When performing subtraction, the result should be reported with the same number of decimal places as the measurement with the least number of decimal places.

### Step 5: Round the result
Since \( 22.4 \) has one decimal place, we round \( 19.857 \, \text{m} \) to one decimal place:
- The first decimal place of \( 19.857 \) is \( 8 \) (which is followed by \( 5 \)), so we round up:
\[ 19.857 \, \text{m} \approx 19.9 \, \text{m} \]

### Final Answer
Thus, the remaining length of the rod, according to the idea of significant figures, is:
\[ \boxed{19.9 \, \text{m}} \]

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