The sum of the numbers 436.32, 227.2 and 0.301 in appropriate significant figures is

Options

A. A. 663.821
B. B. 664
C. C. 663.8
D. D. 663.82

Explanation

To solve the problem of finding the sum of the numbers 436.32, 227.2, and 0.301 in appropriate significant figures, we will follow these steps:

### Step 1: Add the Numbers
First, we need to add the three numbers together.

\[ 436.32 + 227.2 + 0.301 \]

### Step 2: Perform the Addition
Let's perform the addition step by step:

1. Align the numbers by their decimal points:
```
436.320
+ 227.200
+ 0.301
___________
```

2. Now, add them column by column:
- Starting from the rightmost column (thousandths place):
- \(0 + 0 + 1 = 1\)
- Next column (hundredths place):
- \(2 + 0 + 0 = 2\)
- Next column (tenths place):
- \(3 + 2 + 3 = 8\)
- Next column (units place):
- \(6 + 7 + 0 = 13\) (write down 3 and carry over 1)
- Next column (tens place):
- \(3 + 2 + 1 = 6\) (including the carry over)
- Finally, the hundreds place:
- \(4 + 2 = 6\)

So, the total sum is:

\[ 663.821 \]

### Step 3: Determine the Significant Figures
Next, we need to round the result to the appropriate number of significant figures based on the original numbers.

- The number 436.32 has **2 decimal places**.
- The number 227.2 has **1 decimal place**.
- The number 0.301 has **3 decimal places**.

The number with the least decimal places is **227.2**, which has **1 decimal place**.

### Step 4: Round the Result
Now, we round 663.821 to **1 decimal place**:

- Look at the first decimal place: \(8\)
- Look at the second decimal place: \(2\) (which is less than 5)

Since the second decimal place is less than 5, we do not round up.

Thus, the rounded result is:

\[ 663.8 \]

### Final Answer
The sum of the numbers 436.32, 227.2, and 0.301 in appropriate significant figures is **663.8**.

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