Perform the following calculations to the appropriate number of signficiant digits `2.6xx10^(3)+2.4xx10^(2)-1.4xx10^(2)`

Answer

To solve the problem \(2.6 \times 10^{3} + 2.4 \times 10^{2} - 1.4 \times 10^{2}\) while considering significant figures, we will follow these steps:

### Step 1: Identify the terms and their significant figures
The terms given are:
- \(2.6 \times 10^{3}\) (2 significant figures)
- \(2.4 \times 10^{2}\) (2 significant figures)
- \(1.4 \times 10^{2}\) (2 significant figures)

### Step 2: Convert all terms to the same power of ten
To simplify the addition and subtraction, we will convert all terms to the same exponent. We can convert \(2.6 \times 10^{3}\) to the same power as the other two terms:

\[ 2.6 \times 10^{3} = 26.0 \times 10^{2} \]

Now, we can rewrite the expression as:
\[ 26.0 \times 10^{2} + 2.4 \times 10^{2} - 1.4 \times 10^{2} \]

### Step 3: Combine the terms
Now we can combine the terms:
\[ (26.0 + 2.4 - 1.4) \times 10^{2} \]

Calculating the values inside the parentheses:
\[ 26.0 + 2.4 = 28.4 \]
\[ 28.4 - 1.4 = 27.0 \]

So we have:
\[ 27.0 \times 10^{2} \]

### Step 4: Convert back to scientific notation
Now we convert \(27.0 \times 10^{2}\) back to scientific notation:
\[ 2.70 \times 10^{3} \]

### Step 5: Determine the significant figures
Since all the original numbers had 2 significant figures, we will round our final answer to 2 significant figures. Thus, \(2.70 \times 10^{3}\) becomes:
\[ 2.7 \times 10^{3} \]

### Final Answer
The final answer is:
\[ \boxed{2.7 \times 10^{3}} \]