Question

show the calculator answer, significant digits answer and identify the number of significant digits. show all work.
65000(0.08 x 200 x 0.004) / (800 x 300)

make it more clear.

Answer 1

To break down the calculation \( \frac{65000 \times (0.08 \times 200 \times 0.004)}{800 \times 300} \) into clear parts, we'll follow these steps:

### Step 1: Calculate the Numerator

First, we will calculate the expression inside the parentheses:

1. **Calculate \( 0.08 \times 200 \):**
\[
0.08 \times 200 = 16
\]
- **Significant digits:** \( 0.08 \) has **2 significant figures**, \( 200 \) has **1 significant figure** (the trailing zeros are not counted unless there is a decimal point). The result \( 16 \) is reported with **1 significant figure**, so it rounds to **10** when considering significant figures.

2. **Calculate \( 10 \times 0.004\):**
\[
10 \times 0.004 = 0.04
\]
- **Significant digits:** \( 10 \) has **1 significant figure**, \( 0.004 \) has **1 significant figure**. The result is **0.04**, which is reported with **1 significant figure**.

Now, we multiply it with \( 65000 \):

3. **Calculate \( 65000 \times 0.04\):**
\[
65000 \times 0.04 = 2600
\]
- **Significant digits:** \( 65000 \) has **2 significant figures** (inserting a decimal point could clarify), and \( 0.04 \) has **1 significant figure**. The result \( 2600 \) will be rounded to **2600** (as it is already in a satisfactory format consistent with 1 significant figure).

### Step 2: Calculate the Denominator

Calculate \( 800 \times 300 \):

1. **Calculate \( 800 \times 300 \):**
\[
800 \times 300 = 240000
\]
- **Significant digits:** \( 800 \) has **1 significant figure** (again due to trailing zeros), and \( 300 \) has **1 significant figure**, so the result is reported as **240000** with **1 significant figure**.

### Step 3: Complete the Calculation

Now we have:

- Numerator: \( 2600 \) (1 significant figure)
- Denominator: \( 240000 \) (1 significant figure)

Thus we can write:

\[
\frac{2600}{240000}
\]

Calculate the division:

\[
\frac{2600}{240000} = 0.0108333
\]

### Step 4: Adjust for Significant Figures

Given both the numerator and denominator have only **1 significant figure**, we round the result to **1 significant figure**:

\[
0.0108333 \rightarrow 0.01
\]

This retains only **1 significant figure**.

### Summary

- **Calculator Answer:** \( 0.0108333 \)
- **Significant Digits Answer:** \( 0.01 \)
- **Number of Significant Digits in Final Answer:** 1 significant figure.

### Final Result

\[
\text{Final Answer: } 0.01
\]