Three measurements are a = 483, b=73.67 and c=15.67. Find the value `(ab)/(c)` to correct significant figures.

Explanation

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

### Step 1: Identify the significant figures of each measurement
- Measurement \(a = 483\): This has **3 significant figures**.
- Measurement \(b = 73.67\): This has **4 significant figures**.
- Measurement \(c = 15.67\): This also has **4 significant figures**.

### Step 2: Determine the limiting factor for significant figures
The number of significant figures in the final result will be determined by the measurement with the least significant figures. Here, \(a\) has the least significant figures (3 significant figures).

### Step 3: Calculate the value of \((ab)/c\)
First, we calculate \(ab\):
\[ ab = 483 \times 73.67 \]
Calculating this gives:
\[ ab = 35608.81 \]

Next, we divide \(ab\) by \(c\):
\[ \frac{ab}{c} = \frac{35608.81}{15.67} \]
Calculating this gives:
\[ \frac{ab}{c} \approx 2270.75 \]

### Step 4: Round the result to the correct number of significant figures
Since \(a\) has the least significant figures (3), we need to round \(2270.75\) to **3 significant figures**.

The first three significant figures of \(2270.75\) are \(227\). The next digit is \(0\), which is less than \(5\), so we round down:
\[ 2270.75 \rightarrow 2270 \]

### Step 5: Express the final answer in scientific notation
To express \(2270\) in scientific notation with 3 significant figures:
\[ 2270 = 2.27 \times 10^3 \]

### Final Answer
Thus, the value of \((ab)/c\) to the correct significant figures is:
\[ \boxed{2.27 \times 10^3} \]

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