Three measurements are, a= 25.6, b=21.1 and c=2.43. Find the value of a-b-c to correct significant figures.

Explanation

To solve the problem of finding the value of \( a - b - c \) with the correct significant figures, we will follow these steps:

### Step 1: Identify the given values
We have the following measurements:
- \( a = 25.6 \)
- \( b = 21.1 \)
- \( c = 2.43 \)

### Step 2: Perform the subtraction
We need to calculate \( a - b - c \):
\[ a - b - c = 25.6 - 21.1 - 2.43 \]

### Step 3: Calculate \( a - b \)
First, we subtract \( b \) from \( a \):
\[ 25.6 - 21.1 = 4.5 \]

### Step 4: Subtract \( c \) from the result
Now we subtract \( c \) from the result of \( a - b \):
\[ 4.5 - 2.43 = 2.07 \]

### Step 5: Determine the correct significant figures
Now we need to round \( 2.07 \) to the correct number of significant figures.

- The number \( 25.6 \) has **one decimal place**.
- The number \( 21.1 \) also has **one decimal place**.
- The number \( 2.43 \) has **two decimal places**.

When performing addition or subtraction, the result should be rounded to the least number of decimal places among the values involved in the calculation. Here, \( a \) and \( b \) both have one decimal place, which is the least among the three measurements.

### Step 6: Round the result
Thus, we round \( 2.07 \) to one decimal place:
\[ 2.07 \approx 2.1 \]

### Final Answer
The final result of \( a - b - c \) to the correct significant figures is:
\[ \boxed{2.1} \]

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