Question

show the calculator answer, significant digits answer and identify the number of significant digits. show all work.
338855.0 +
10000000.003
make it more clear.

Answer 1

To solve the problem \( 338855.0 + 10000000.003 \) while considering significant digits, let's break down the process step by step.

### Step 1: Align the Numbers
To add the numbers, we'll align them by the decimal point:

```
338855.0
+ 10000000.003
```

### Step 2: Perform the Addition
Adding the numbers gives us:

```
338855.0
+ 10000000.003
---------------
10338855.003
```

### Step 3: Determine the Significant Digits
**Significant digits** refer to the number of digits that carry meaning contributing to its precision. The rules for determining the number of significant figures in addition or subtraction are as follows:

1. The result should be rounded to the same decimal place as the measurement with the least precision (i.e., the smallest number of digits to the right of the decimal).

**Analyzing the two quantities:**
- \( 338855.0 \) has **7 significant digits** (because of the trailing zero after the decimal point).
- \( 10000000.003 \) has **11 significant digits** (because all non-zero and counted digits are significant).

The number \( 338855.0 \) has a decimal place at the first decimal (one digit after the decimal point), which is the most precise measurement of the two.

### Step 4: Round the Result
Since the number \( 338855.0 \) has one digit after the decimal, we will round our result \( 10338855.003 \) to one decimal place.

Rounding \( 10338855.003 \) to one decimal place gives us:
- The digit in the tenths place is \( 3 \) and the next digit (hundredths place) is \( 0 \), which means we do not round up.

Thus, our result becomes \( 10338855.0 \).

### Final Summary
1. **Calculator Answer**: \( 10338855.003 \)
2. **Final Answer with Significant Digits**: \( 10338855.0 \)
3. **Number of Significant Digits in Final Answer**: **8 significant digits**

So, the summary of the work is as follows:

\[
338855.0 + 10000000.003 = 10338855.003 \quad (\text{calculator answer})
\]
Rounding based on significant digits:
\[
\text{Final Answer} = 10338855.0 \quad (\text{with 8 significant digits})
\]