show the calculator answer, significant digits answer and identify the number of significant digits. show all work.

Question

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

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