To solve the expression \(4.35 \times 2.74 \times 3.008\) and identify significant digits, we will follow these steps:
Step 1: Perform the Calculation
We first calculate the product:
\[ 4.35 \times 2.74 = 11.907 \]
Now, we will multiply this result by \(3.008\):
\[ 11.907 \times 3.008 = 35.818056 \]
Step 2: Identify Significant Digits
Next, we need to determine the number of significant digits for each of the numbers involved:
-
4.35:
- It has 3 significant digits (all non-zero digits are significant).
-
2.74:
- It has 3 significant digits (all non-zero digits are significant).
-
3.008:
- It has 4 significant digits (the leading zero is not significant, but all other digits are).
Step 3: Determine the Result with the Correct Number of Significant Digits
According to rules for multiplication, the result should be reported with the same number of significant digits as the value in the calculation with the least number of significant digits. Here, the least is 3 significant digits (from both 4.35 and 2.74).
Step 4: Round the Result
The unrounded product we calculated is \(35.818056\). We round this to 3 significant digits:
- The first three digits are 358.
- The next digit after the first three is 1, which is less than 5, so we do not round up.
Thus,
\[ 35.818056 \text{ rounded to 3 significant digits is } 35.8. \]
Final Result
- Calculator Answer: \(35.818056\)
- Significant Digits Answer: \(35.8\)
- Number of Significant Digits: 3
Summary
\[ 4.35 \times 2.74 \times 3.008 = 35.818056 \quad (\text{calculator answer}) \] \[ \text{Rounded to 3 significant digits: } 35.8 \quad (\text{significant digits answer}) \] \[ \text{Number of significant digits: } 3 \]